internlm/Lean-Github huggingface dataset:
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
⊢ f.assignments[↑i] = unassigned
Tactic:
simp only [l'] at l'_eq_true
Proof state after:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
⊢ f.assignments[↑i] = unassigned
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
⊢ f.assignments[↑i] = unassigned
Tactic:
simp only [hasAssignment, l'_eq_true, ite_true] at h2
Proof state after:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
h2 : ¬f.assignments[↑i].hasPosAssignment = true
⊢ f.assignments[↑i] = unassigned
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
h2 : ¬f.assignments[↑i].hasPosAssignment = true
⊢ f.assignments[↑i] = unassigned
Tactic:
simp only [hasAssignment, l_eq_false, ↓reduceIte, getElem!, l_eq_i, i_in_bounds,
  Array.get_eq_getElem, h1, addAssignment, l'_eq_true, hasNeg_of_addPos] at h
Proof state after:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
h2 : ¬f.assignments[↑i].hasPosAssignment = true
h : ¬f.assignments[↑i].hasNegAssignment = true
⊢ f.assignments[↑i] = unassigned
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.left
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : (acc.snd.fst.get j).snd = true
h2 : ¬f.assignments[↑i].hasPosAssignment = true
h : ¬f.assignments[↑i].hasNegAssignment = true
⊢ f.assignments[↑i] = unassigned
Tactic:
exact unassigned_of_has_neither _ h2 h
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.right
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
⊢ ∀ (k : Fin acc.snd.fst.length.succ),
    ¬k = ⟨↑j + 1, j_succ_in_bounds⟩ → ¬k = ⟨0, zero_in_bounds⟩ → ¬((l :: acc.snd.fst).get k).fst.val = ↑i
Tactic:
intro k k_ne_j_succ k_ne_zero
Proof state after:
case right.right.right.right
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get k).fst.val = ↑i
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.right
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k_eq_succ : ∃ k' k'_succ_in_bounds, k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get k).fst.val = ↑i
Tactic:
rcases k_eq_succ with ⟨k', k'_succ_in_bounds, k_eq_succ⟩
Proof state after:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get k).fst.val = ↑i
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get k).fst.val = ↑i
Tactic:
rw [k_eq_succ]
Proof state after:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get ⟨k' + 1, k'_succ_in_bounds⟩).fst.val = ↑i
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬((l :: acc.snd.fst).get ⟨k' + 1, k'_succ_in_bounds⟩).fst.val = ↑i
Tactic:
simp only [List.get, Nat.add_eq, Nat.add_zero, ne_eq]
Proof state after:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬(acc.snd.fst.get ⟨k', ⋯⟩).fst.val = ↑i
Theorem: LRAT.DefaultFormula.confirmRupHint_preserves_invariant_helper
Proof state before:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
⊢ ¬(acc.snd.fst.get ⟨k', ⋯⟩).fst.val = ↑i
Tactic:
have k'_in_bounds : k' < acc.2.1.length := by
  simp only [List.length_cons, Nat.succ_eq_add_one] at k'_succ_in_bounds
  exact Nat.lt_of_succ_lt_succ k'_succ_in_bounds
Proof state after:
case right.right.right.right.intro.intro
n : Nat
f : DefaultFormula n
f_assignments_size : f.assignments.size = n
acc : Array Assignment × List (Literal (PosFin n)) × Bool × Bool
hsize : acc.fst.size = n
l : Literal (PosFin n)
ih : f.derivedLits_invariant f_assignments_size acc.fst hsize acc.snd.fst
h : ¬hasAssignment l.snd acc.fst[l.fst.val]! = true
hsize'✝ : (acc.fst.modify l.fst.val (addAssignment l.snd)).size = n :=
  Eq.mpr (id (congrArg (fun _a => _a = n) Array.modify_preserves_size)) hsize
i : Fin n
i_in_bounds : ↑i < acc.fst.size
l_in_bounds : l.fst.val < acc.fst.size
j : Fin acc.snd.fst.length
j_eq_i : (acc.snd.fst.get j).fst.val = ↑i
h1 : acc.fst[↑i] = addAssignment (acc.snd.fst.get j).snd f.assignments[↑i]
h2 : ¬hasAssignment (acc.snd.fst.get j).snd f.assignments[↑i] = true
h3 : ∀ (k : Fin acc.snd.fst.length), k ≠ j → (acc.snd.fst.get k).fst.val ≠ ↑i
l' : Literal (PosFin n) := acc.snd.fst.get j
zero_in_bounds : 0 < (l :: acc.snd.fst).length
j_succ_in_bounds : ↑j + 1 < (l :: acc.snd.fst).length
l_eq_i : l.fst.val = ↑i
l_ne_l' : false ≠ l'.snd
l_eq_false : l.snd = false
l'_eq_true : l'.snd = true
k : Fin acc.snd.fst.length.succ
k_ne_j_succ : ¬k = ⟨↑j + 1, j_succ_in_bounds⟩
k_ne_zero : ¬k = ⟨0, zero_in_bounds⟩
k' : Nat
k'_succ_in_bounds : k' + 1 < (l :: acc.snd.fst).length
k_eq_succ : k = ⟨k' + 1, k'_succ_in_bounds⟩
k'_in_bounds : k' < acc.snd.fst.length
⊢ ¬(acc.snd.fst.get ⟨k', ⋯⟩).fst.val = ↑i