Theorem: LRAT.DefaultFormula.insertRupUnits_preserves_assignments_invariant (LeanSAT/LRAT/Formula/RupAddSound.lean)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
⊢ (f.insertRupUnits units).fst.assignments_invariant
Tactic:
have h := insertRupUnits_postcondition f f_readyForRupAdd units
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
⊢ (f.insertRupUnits units).fst.assignments_invariant

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
⊢ (f.insertRupUnits units).fst.assignments_invariant
Tactic:
have hsize : (insertRupUnits f units).1.assignments.size = n := by rw [insertRupUnits_preserves_assignments_size, f_readyForRupAdd.2.1]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
⊢ (f.insertRupUnits units).fst.assignments_invariant

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
⊢ (f.insertRupUnits units).fst.assignments_invariant
Tactic:
apply Exists.intro hsize
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
⊢ ∀ (i : PosFin n) (b : Bool),
    hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true →
      limplies (PosFin n) (f.insertRupUnits units).fst (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
⊢ ∀ (i : PosFin n) (b : Bool),
    hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true →
      limplies (PosFin n) (f.insertRupUnits units).fst (i, b)
Tactic:
intro i b hb p hp
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp : p ⊨ (f.insertRupUnits units).fst
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ((f.insertRupUnits units).fst.toList.all fun s =>
      decide (((Clause.toList s).any fun l => decide (p l.fst = l.snd)) = true)) =
    true
⊢ p ⊨ (i, b)
Tactic:
simp only [toList, Array.toList_eq, List.append_assoc, List.any_eq_true, Prod.exists,
  Bool.exists_bool, Bool.decide_coe, List.all_eq_true, List.mem_append, List.mem_filterMap, id_eq,
  exists_eq_right, List.mem_map] at hp
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
⊢ p ⊨ (i, b)
Tactic:
rcases h ⟨i.1, i.2.2⟩ with ⟨h1, h2⟩ | ⟨j, b', i_gt_zero, h1, h2, h3, h4⟩ | ⟨j1, j2, i_gt_zero, h1, h2, _, _, _⟩
State after:
case inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
h1 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = f.assignments[↑⟨i.val, ⋯⟩]
h2 :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size), (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

State before:
case inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
h1 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = f.assignments[↑⟨i.val, ⋯⟩]
h2 :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size), (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
. rw [h1] at hb
  exact (assignments_invariant_of_strong_assignments_invariant f f_readyForRupAdd.2).2 i b hb p pf
State after:
case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

State before:
case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
. rw [h2] at hb
  by_cases b = b'
  . next b_eq_b' =>
    let j_unit := unit (insertRupUnits f units).1.rupUnits[j]
    have j_unit_def : j_unit = unit (insertRupUnits f units).1.rupUnits[j] := rfl
    have j_unit_in_insertRupUnits_res :
      ∃ i : PosFin n,
        (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j_unit ∨
        (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j_unit := by
      apply Exists.intro i
      rw [j_unit_def, h1]
      by_cases hb' : b'
      . rw [hb']
        apply Or.inr
        constructor
        . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
            rw [hb'] at h1
            rw [h1]
            simp only [Prod.mk.injEq, and_true]
            apply Subtype.ext
            rfl
          rw [← h1]
          apply Array.getElem_mem_data
        . rfl
      . simp only [Bool.not_eq_true] at hb'
        rw [hb']
        apply Or.inl
        constructor
        . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, false) := by
            rw [hb'] at h1
            rw [h1]
            simp only [Prod.mk.injEq, and_true]
            apply Subtype.ext
            rfl
          rw [← h1]
          apply Array.getElem_mem_data
        . rfl
    specialize hp j_unit ((Or.inr ∘ Or.inl) j_unit_in_insertRupUnits_res)
    simp only [List.any_eq_true, Prod.exists, Bool.exists_bool, Bool.decide_coe, Fin.getElem_fin, List.find?, j_unit] at hp
    simp only [Fin.getElem_fin] at h1
    rcases hp with ⟨i', hp⟩
    simp only [h1, Clause.toList, unit_eq, List.mem_singleton,
      Prod.mk.injEq] at hp
    rcases hp with ⟨hp1, hp2⟩ | ⟨hp1, hp2⟩
    . simp only [b_eq_b', ← hp1.2, HSat.eval]
      rw [hp1.1] at hp2
      exact of_decide_eq_true hp2
    . simp only [b_eq_b', ← hp1.2, HSat.eval]
      rw [hp1.1] at hp2
      exact hp2
  . next b_ne_b' =>
    apply (assignments_invariant_of_strong_assignments_invariant f f_readyForRupAdd.2).2 i b _ p pf
    have b'_def : b' = (decide ¬b = true) := by
      cases b <;> cases b' <;> simp at *
    rw [has_iff_has_of_add_complement, ← b'_def, hb]
State after:
case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

State before:
case inr.inr.intro.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j1 j2 : Fin (f.insertRupUnits units).fst.rupUnits.size
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j1] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.rupUnits[j2] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, false)
left✝¹ : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = both
left✝ : f.assignments[↑⟨i.val, ⋯⟩] = unassigned
right✝ :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j1 → k ≠ j2 → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
. let j1_unit := unit (insertRupUnits f units).1.rupUnits[j1]
  have j1_unit_def : j1_unit = unit (insertRupUnits f units).1.rupUnits[j1] := rfl
  have j1_unit_in_insertRupUnits_res :
    ∃ i : PosFin n,
      (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j1_unit ∨
      (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j1_unit := by
    apply Exists.intro i ∘ Or.inr
    rw [j1_unit_def, h1]
    constructor
    . have h1 : (insertRupUnits f units).fst.rupUnits[j1] = (i, true) := by
        rw [h1]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h1]
      apply Array.getElem_mem_data
    . rfl
  let j2_unit := unit (insertRupUnits f units).1.rupUnits[j2]
  have j2_unit_def : j2_unit = unit (insertRupUnits f units).1.rupUnits[j2] := rfl
  have j2_unit_in_insertRupUnits_res :
    ∃ i : PosFin n,
      (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j2_unit ∨
      (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j2_unit := by
    apply Exists.intro i ∘ Or.inl
    rw [j2_unit_def, h2]
    constructor
    . have h2 : (insertRupUnits f units).fst.rupUnits[j2] = (i, false) := by
        rw [h2]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h2]
      apply Array.getElem_mem_data
    . rfl
  have hp1 := hp j1_unit ((Or.inr ∘ Or.inl) j1_unit_in_insertRupUnits_res)
  have hp2 := hp j2_unit ((Or.inr ∘ Or.inl) j2_unit_in_insertRupUnits_res)
  simp only [List.any_eq_true, Prod.exists, Bool.exists_bool, Bool.decide_coe, Fin.getElem_fin, List.find?, j1_unit, j2_unit] at hp1 hp2
  rcases hp1 with ⟨i1, hp1⟩
  rcases hp2 with ⟨i2, hp2⟩
  simp only [Fin.getElem_fin] at h1
  simp only [Fin.getElem_fin] at h2
  simp only [h1, Clause.toList, unit_eq, List.mem_singleton, Prod.mk.injEq,
    and_false, false_and, and_true, false_or, h2, or_false] at hp1 hp2
  simp only [hp2.1, ← hp1.1, decide_eq_true_eq, true_and] at hp2
  simp only [hp1.2] at hp2
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
⊢ (f.insertRupUnits units).fst.assignments.size = n
Tactic:
rw [insertRupUnits_preserves_assignments_size, f_readyForRupAdd.2.1]
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
⊢ (f.toList.all fun s => decide (((Clause.toList s).any fun l => decide (p l.fst = l.snd)) = true)) = true
Tactic:
simp only [toList, Array.toList_eq, List.append_assoc, List.any_eq_true, Prod.exists, Bool.exists_bool,
  Bool.decide_coe, List.all_eq_true, List.mem_append, List.mem_filterMap, id_eq, exists_eq_right, List.mem_map]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
⊢ ∀ (x : DefaultClause n),
    (some x ∈ f.clauses.data ∨
        (∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = x ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = x ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
⊢ ∀ (x : DefaultClause n),
    (some x ∈ f.clauses.data ∨
        (∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = x ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = x ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
Tactic:
intro c cf
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf :
  some c ∈ f.clauses.data ∨
    (∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c) ∨
      ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf :
  some c ∈ f.clauses.data ∨
    (∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c) ∨
      ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
rcases cf with cf | cf | cf
State after:
case inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : some c ∈ f.clauses.data
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
case inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : some c ∈ f.clauses.data
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
. specialize hp c (Or.inl cf)
  exact hp
State after:
case inr.inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
case inr.inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
. simp only [f_readyForRupAdd.1, Array.data_toArray, List.find?, List.not_mem_nil, false_and, or_self, exists_false] at cf
State after:
case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
. specialize hp c $ (Or.inr ∘ Or.inr) cf
  exact hp
State after:
no goals

State before:
case inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : some c ∈ f.clauses.data
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
specialize hp c (Or.inl cf)
State after:
case inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
c : DefaultClause n
cf : some c ∈ f.clauses.data
hp : ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
case inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
c : DefaultClause n
cf : some c ∈ f.clauses.data
hp : ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
exact hp
State after:
no goals

State before:
case inr.inl
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.rupUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.rupUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
simp only [f_readyForRupAdd.1, Array.data_toArray, List.find?, List.not_mem_nil, false_and, or_self, exists_false] at cf
State after:
no goals

State before:
case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
specialize hp c $ (Or.inr ∘ Or.inr) cf
State after:
case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
hp : ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true

State before:
case inr.inr
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
c : DefaultClause n
cf : ∃ a, (a, false) ∈ f.ratUnits.data ∧ unit (a, false) = c ∨ (a, true) ∈ f.ratUnits.data ∧ unit (a, true) = c
hp : ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
⊢ ∃ a, (a, false) ∈ Clause.toList c ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList c ∧ p a = true
Tactic:
exact hp
State after:
no goals

State before:
case inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
h1 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = f.assignments[↑⟨i.val, ⋯⟩]
h2 :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size), (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
rw [h1] at hb
State after:
case inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b f.assignments[↑⟨i.val, ⋯⟩] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
h1 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = f.assignments[↑⟨i.val, ⋯⟩]
h2 :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size), (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

State before:
case inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b f.assignments[↑⟨i.val, ⋯⟩] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
h1 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = f.assignments[↑⟨i.val, ⋯⟩]
h2 :
  ∀ (j : Fin (f.insertRupUnits units).fst.rupUnits.size), (f.insertRupUnits units).fst.rupUnits[j].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
exact (assignments_invariant_of_strong_assignments_invariant f f_readyForRupAdd.2).2 i b hb p pf
State after:
no goals

State before:
case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.insertRupUnits units).fst.assignments[i.val] = true
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
rw [h2] at hb
State after:
case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)

State before:
case inr.inl.intro.intro.intro.intro.intro.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
⊢ p ⊨ (i, b)
Tactic:
by_cases b = b'
State after:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : b = b'
⊢ p ⊨ (i, b)

case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : ¬b = b'
⊢ p ⊨ (i, b)

State before:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : b = b'
⊢ p ⊨ (i, b)

case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : ¬b = b'
⊢ p ⊨ (i, b)
Tactic:
. next b_eq_b' =>
  let j_unit := unit (insertRupUnits f units).1.rupUnits[j]
  have j_unit_def : j_unit = unit (insertRupUnits f units).1.rupUnits[j] := rfl
  have j_unit_in_insertRupUnits_res :
    ∃ i : PosFin n,
      (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j_unit := by
    apply Exists.intro i
    rw [j_unit_def, h1]
    by_cases hb' : b'
    . rw [hb']
      apply Or.inr
      constructor
      . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
          rw [hb'] at h1
          rw [h1]
          simp only [Prod.mk.injEq, and_true]
          apply Subtype.ext
          rfl
        rw [← h1]
        apply Array.getElem_mem_data
      . rfl
    . simp only [Bool.not_eq_true] at hb'
      rw [hb']
      apply Or.inl
      constructor
      . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, false) := by
          rw [hb'] at h1
          rw [h1]
          simp only [Prod.mk.injEq, and_true]
          apply Subtype.ext
          rfl
        rw [← h1]
        apply Array.getElem_mem_data
      . rfl
  specialize hp j_unit ((Or.inr ∘ Or.inl) j_unit_in_insertRupUnits_res)
  simp only [List.any_eq_true, Prod.exists, Bool.exists_bool, Bool.decide_coe, Fin.getElem_fin, List.find?, j_unit] at hp
  simp only [Fin.getElem_fin] at h1
  rcases hp with ⟨i', hp⟩
  simp only [h1, Clause.toList, unit_eq, List.mem_singleton,
    Prod.mk.injEq] at hp
  rcases hp with ⟨hp1, hp2⟩ | ⟨hp1, hp2⟩
  . simp only [b_eq_b', ← hp1.2, HSat.eval]
    rw [hp1.1] at hp2
    exact of_decide_eq_true hp2
  . simp only [b_eq_b', ← hp1.2, HSat.eval]
    rw [hp1.1] at hp2
    exact hp2
State after:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : ¬b = b'
⊢ p ⊨ (i, b)

State before:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : ¬b = b'
⊢ p ⊨ (i, b)
Tactic:
. next b_ne_b' =>
  apply (assignments_invariant_of_strong_assignments_invariant f f_readyForRupAdd.2).2 i b _ p pf
  have b'_def : b' = (decide ¬b = true) := by
    cases b <;> cases b' <;> simp at *
  rw [has_iff_has_of_add_complement, ← b'_def, hb]
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
h✝ : b = b'
⊢ p ⊨ (i, b)
Tactic:
next b_eq_b' =>
let j_unit := unit (insertRupUnits f units).1.rupUnits[j]
have j_unit_def : j_unit = unit (insertRupUnits f units).1.rupUnits[j] := rfl
have j_unit_in_insertRupUnits_res :
  ∃ i : PosFin n,
    (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j_unit ∨
    (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j_unit := by
  apply Exists.intro i
  rw [j_unit_def, h1]
  by_cases hb' : b'
  . rw [hb']
    apply Or.inr
    constructor
    . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
        rw [hb'] at h1
        rw [h1]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h1]
      apply Array.getElem_mem_data
    . rfl
  . simp only [Bool.not_eq_true] at hb'
    rw [hb']
    apply Or.inl
    constructor
    . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, false) := by
        rw [hb'] at h1
        rw [h1]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h1]
      apply Array.getElem_mem_data
    . rfl
specialize hp j_unit ((Or.inr ∘ Or.inl) j_unit_in_insertRupUnits_res)
simp only [List.any_eq_true, Prod.exists, Bool.exists_bool, Bool.decide_coe, Fin.getElem_fin, List.find?, j_unit] at hp
simp only [Fin.getElem_fin] at h1
rcases hp with ⟨i', hp⟩
simp only [h1, Clause.toList, unit_eq, List.mem_singleton,
  Prod.mk.injEq] at hp
rcases hp with ⟨hp1, hp2⟩ | ⟨hp1, hp2⟩
. simp only [b_eq_b', ← hp1.2, HSat.eval]
  rw [hp1.1] at hp2
  exact of_decide_eq_true hp2
. simp only [b_eq_b', ← hp1.2, HSat.eval]
  rw [hp1.1] at hp2
  exact hp2
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
⊢ p ⊨ (i, b)
Tactic:
let j_unit := unit (insertRupUnits f units).1.rupUnits[j]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ p ⊨ (i, b)
Tactic:
have j_unit_def : j_unit = unit (insertRupUnits f units).1.rupUnits[j] := rfl
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ p ⊨ (i, b)
Tactic:
have j_unit_in_insertRupUnits_res :
  ∃ i : PosFin n,
    (i, false) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, false) = j_unit ∨
    (i, true) ∈ (insertRupUnits f units).1.rupUnits.data ∧ unit (i, true) = j_unit := by
  apply Exists.intro i
  rw [j_unit_def, h1]
  by_cases hb' : b'
  . rw [hb']
    apply Or.inr
    constructor
    . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
        rw [hb'] at h1
        rw [h1]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h1]
      apply Array.getElem_mem_data
    . rfl
  . simp only [Bool.not_eq_true] at hb'
    rw [hb']
    apply Or.inl
    constructor
    . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, false) := by
        rw [hb'] at h1
        rw [h1]
        simp only [Prod.mk.injEq, and_true]
        apply Subtype.ext
        rfl
      rw [← h1]
      apply Array.getElem_mem_data
    . rfl
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
⊢ p ⊨ (i, b)
Tactic:
specialize hp j_unit ((Or.inr ∘ Or.inl) j_unit_in_insertRupUnits_res)
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a, (a, false) ∈ Clause.toList j_unit ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList j_unit ∧ p a = true
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a, (a, false) ∈ Clause.toList j_unit ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList j_unit ∧ p a = true
⊢ p ⊨ (i, b)
Tactic:
simp only [List.any_eq_true, Prod.exists, Bool.exists_bool, Bool.decide_coe, Fin.getElem_fin, List.find?, j_unit] at hp
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a,
    (a, false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p a = false) = true ∨
      (a, true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p a = true
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a,
    (a, false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p a = false) = true ∨
      (a, true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p a = true
⊢ p ⊨ (i, b)
Tactic:
simp only [Fin.getElem_fin] at h1
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a,
    (a, false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p a = false) = true ∨
      (a, true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p a = true
⊢ p ⊨ (i, b)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
hp :
  ∃ a,
    (a, false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p a = false) = true ∨
      (a, true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p a = true
⊢ p ⊨ (i, b)
Tactic:
rcases hp with ⟨i', hp⟩
State after:
case intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp :
  (i', false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p i' = false) = true ∨
    (i', true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p i' = true
⊢ p ⊨ (i, b)

State before:
case intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp :
  (i', false) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ decide (p i' = false) = true ∨
    (i', true) ∈ Clause.toList (unit (f.insertRupUnits units).fst.rupUnits[↑j]) ∧ p i' = true
⊢ p ⊨ (i, b)
Tactic:
simp only [h1, Clause.toList, unit_eq, List.mem_singleton,
  Prod.mk.injEq] at hp
State after:
case intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp : (i' = ⟨i.val, ⋯⟩ ∧ false = b') ∧ decide (p i' = false) = true ∨ (i' = ⟨i.val, ⋯⟩ ∧ true = b') ∧ p i' = true
⊢ p ⊨ (i, b)

State before:
case intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp : (i' = ⟨i.val, ⋯⟩ ∧ false = b') ∧ decide (p i' = false) = true ∨ (i' = ⟨i.val, ⋯⟩ ∧ true = b') ∧ p i' = true
⊢ p ⊨ (i, b)
Tactic:
rcases hp with ⟨hp1, hp2⟩ | ⟨hp1, hp2⟩
State after:
case intro.inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ false = b'
hp2 : decide (p i' = false) = true
⊢ p ⊨ (i, b)

case intro.inr.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ true = b'
hp2 : p i' = true
⊢ p ⊨ (i, b)

State before:
case intro.inl.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ false = b'
hp2 : decide (p i' = false) = true
⊢ p ⊨ (i, b)

case intro.inr.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ true = b'
hp2 : p i' = true
⊢ p ⊨ (i, b)
Tactic:
. simp only [b_eq_b', ← hp1.2, HSat.eval]
  rw [hp1.1] at hp2
  exact of_decide_eq_true hp2
State after:
case intro.inr.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ true = b'
hp2 : p i' = true
⊢ p ⊨ (i, b)

State before:
case intro.inr.intro
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[↑j] = (⟨i.val, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_in_insertRupUnits_res :
  ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
i' : PosFin n
hp1 : i' = ⟨i.val, ⋯⟩ ∧ true = b'
hp2 : p i' = true
⊢ p ⊨ (i, b)
Tactic:
. simp only [b_eq_b', ← hp1.2, HSat.eval]
  rw [hp1.1] at hp2
  exact hp2
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ ∃ i,
    (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
      (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
Tactic:
apply Exists.intro i
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = j_unit ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = j_unit
Tactic:
rw [j_unit_def, h1]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
Tactic:
by_cases hb' : b'
State after:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')

case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : ¬b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')

State before:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')

case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : ¬b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
Tactic:
. rw [hb']
  apply Or.inr
  constructor
  . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
      rw [hb'] at h1
      rw [h1]
      simp only [Prod.mk.injEq, and_true]
      apply Subtype.ext
      rfl
    rw [← h1]
    apply Array.getElem_mem_data
  . rfl
State after:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : ¬b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')

State before:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : ¬b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
Tactic:
. simp only [Bool.not_eq_true] at hb'
  rw [hb']
  apply Or.inl
  constructor
  . have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, false) := by
      rw [hb'] at h1
      rw [h1]
      simp only [Prod.mk.injEq, and_true]
      apply Subtype.ext
      rfl
    rw [← h1]
    apply Array.getElem_mem_data
  . rfl
State after:
no goals

State before:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
Tactic:
rw [hb']
State after:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true) ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)

State before:
case pos
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true) ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
Tactic:
apply Or.inr
State after:
case pos.h
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)

State before:
case pos.h
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
Tactic:
constructor
State after:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data

case pos.h.right
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)

State before:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data

case pos.h.right
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
Tactic:
. have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
    rw [hb'] at h1
    rw [h1]
    simp only [Prod.mk.injEq, and_true]
    apply Subtype.ext
    rfl
  rw [← h1]
  apply Array.getElem_mem_data
State after:
case pos.h.right
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)

State before:
case pos.h.right
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
Tactic:
. rfl
State after:
no goals

State before:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data
Tactic:
have h1 : (insertRupUnits f units).fst.rupUnits[j] = (i, true) := by
  rw [hb'] at h1
  rw [h1]
  simp only [Prod.mk.injEq, and_true]
  apply Subtype.ext
  rfl
State after:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1✝ : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data

State before:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1✝ : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
⊢ (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data
Tactic:
rw [← h1]
State after:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1✝ : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
⊢ (f.insertRupUnits units).fst.rupUnits[j] ∈ (f.insertRupUnits units).fst.rupUnits.data

State before:
case pos.h.left
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1✝ : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
⊢ (f.insertRupUnits units).fst.rupUnits[j] ∈ (f.insertRupUnits units).fst.rupUnits.data
Tactic:
apply Array.getElem_mem_data
State after:
no goals

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
Tactic:
rw [hb'] at h1
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (f.insertRupUnits units).fst.rupUnits[j] = (i, true)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (f.insertRupUnits units).fst.rupUnits[j] = (i, true)
Tactic:
rw [h1]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true) = (i, true)

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true) = (i, true)
Tactic:
simp only [Prod.mk.injEq, and_true]
State after:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ ⟨i.val, ⋯⟩ = i

State before:
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ ⟨i.val, ⋯⟩ = i
Tactic:
apply Subtype.ext
State after:
case a
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ ⟨i.val, ⋯⟩.val = i.val

State before:
case a
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ ⟨i.val, ⋯⟩.val = i.val
Tactic:
rfl
State after:
no goals

State before:
case pos.h.right
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = true
⊢ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, true)
Tactic:
rfl
State after:
no goals

State before:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : ¬b' = true
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
Tactic:
simp only [Bool.not_eq_true] at hb'
State after:
case neg
n : Nat
f : DefaultFormula n
f_readyForRupAdd : f.readyForRupAdd
units : List (Literal (PosFin n))
h :
  let assignments := (f.insertRupUnits units).fst.assignments;
  let_fun hsize := ⋯;
  let rupUnits := (f.insertRupUnits units).fst.rupUnits;
  insertUnit_invariant f.assignments ⋯ rupUnits assignments hsize
hsize : (f.insertRupUnits units).fst.assignments.size = n
i : PosFin n
b : Bool
p : PosFin n → Bool
hp :
  ∀ (x : DefaultClause n),
    (some x ∈ (f.insertRupUnits units).fst.clauses.data ∨
        (∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (a, true) = x) ∨
          ∃ a,
            (a, false) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, false) = x ∨
              (a, true) ∈ (f.insertRupUnits units).fst.ratUnits.data ∧ unit (a, true) = x) →
      ∃ a, (a, false) ∈ Clause.toList x ∧ decide (p a = false) = true ∨ (a, true) ∈ Clause.toList x ∧ p a = true
pf : p ⊨ f
j : Fin (f.insertRupUnits units).fst.rupUnits.size
b' : Bool
hb : hasAssignment b (addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]) = true
i_gt_zero : ↑⟨i.val, ⋯⟩ > 0
h1 : (f.insertRupUnits units).fst.rupUnits[j] = (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')
h2 : (f.insertRupUnits units).fst.assignments[↑⟨i.val, ⋯⟩] = addAssignment b' f.assignments[↑⟨i.val, ⋯⟩]
h3 : ¬hasAssignment b' f.assignments[↑⟨i.val, ⋯⟩] = true
h4 :
  ∀ (k : Fin (f.insertRupUnits units).fst.rupUnits.size),
    k ≠ j → (f.insertRupUnits units).fst.rupUnits[k].fst.val ≠ ↑⟨i.val, ⋯⟩
b_eq_b' : b = b'
j_unit : DefaultClause n := unit (f.insertRupUnits units).fst.rupUnits[j]
j_unit_def : j_unit = unit (f.insertRupUnits units).fst.rupUnits[j]
hb' : b' = false
⊢ (i, false) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, false) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b') ∨
    (i, true) ∈ (f.insertRupUnits units).fst.rupUnits.data ∧ unit (i, true) = unit (⟨↑⟨i.val, ⋯⟩, ⋯⟩, b')