internlm/Lean-Github huggingface dataset:
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
heq : c.isUnit = none
h : hasAssignment b acc[i.val] = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
exact ih.2 i b h
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
h :
  hasAssignment b
      (match c.isUnit with
        | none => acc
        | some (l, true) => acc.modify l.val addPosAssignment
        | some (l, false) => acc.modify l.val addNegAssignment)[i.val] =
    true
l : PosFin n
heq : c.isUnit = some (l, true)
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
simp only [heq] at h
Proof state after:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
have i_in_bounds : i.1 < acc.size := by simp only [ih.1, i.2.2]
Proof state after:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
have l_in_bounds : l.1 < acc.size := by simp only [ih.1, l.2.2]
Proof state after:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
rcases ih with ⟨hsize, ih⟩
Proof state after:
case intro
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case intro
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
by_cases i = l.1
Proof state after:
case pos
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
h✝ : i.val = l.val
⊢ unit (i, b) ∈ (ofArray arr).toList

case neg
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
h✝ : ¬i.val = l.val
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case neg
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
h✝ : ¬i.val = l.val
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
. next i_ne_l =>
  simp only [Array.get_modify_unchanged l_in_bounds i_in_bounds _ (Ne.symm i_ne_l)] at h
  exact ih i b h
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
⊢ i.val < acc.size
Tactic:
simp only [ih.1, i.2.2]
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
ih : modified_assignments_invariant acc
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
⊢ l.val < acc.size
Tactic:
simp only [ih.1, l.2.2]
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case pos
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
h✝ : i.val = l.val
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
next i_eq_l =>
simp only [i_eq_l, Array.get_modify_at_idx l_in_bounds] at h
by_cases b
. next b_eq_true =>
  rw [isUnit_iff, DefaultClause.toList] at heq
  simp only [toList, ofArray, Array.toList_eq, List.map, List.append_nil, List.mem_filterMap, id_eq, exists_eq_right]
  have i_eq_l : i = l := Subtype.ext i_eq_l
  simp only [unit, b_eq_true, i_eq_l]
  have c_def : c = ⟨c.clause, c.nodupkey, c.nodup⟩ := rfl
  simp only [heq] at c_def
  rw [c_def] at cOpt_in_arr
  exact cOpt_in_arr
. next b_eq_false =>
  simp only [Bool.not_eq_true] at b_eq_false
  simp only [hasAssignment, b_eq_false, ite_false, hasNeg_of_addPos] at h
  specialize ih l false
  simp only [hasAssignment, ite_false] at ih
  rw [b_eq_false, Subtype.ext i_eq_l]
  exact ih h
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
h : hasAssignment b (acc.modify l.val addPosAssignment)[i.val] = true
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
simp only [i_eq_l, Array.get_modify_at_idx l_in_bounds] at h
Proof state after:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
by_cases b
Proof state after:
case pos
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
h✝ : b = true
⊢ unit (i, b) ∈ (ofArray arr).toList

case neg
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
h✝ : ¬b = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case neg
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
h✝ : ¬b = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
. next b_eq_false =>
  simp only [Bool.not_eq_true] at b_eq_false
  simp only [hasAssignment, b_eq_false, ite_false, hasNeg_of_addPos] at h
  specialize ih l false
  simp only [hasAssignment, ite_false] at ih
  rw [b_eq_false, Subtype.ext i_eq_l]
  exact ih h
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
case pos
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
h✝ : b = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
next b_eq_true =>
rw [isUnit_iff, DefaultClause.toList] at heq
simp only [toList, ofArray, Array.toList_eq, List.map, List.append_nil, List.mem_filterMap, id_eq, exists_eq_right]
have i_eq_l : i = l := Subtype.ext i_eq_l
simp only [unit, b_eq_true, i_eq_l]
have c_def : c = ⟨c.clause, c.nodupkey, c.nodup⟩ := rfl
simp only [heq] at c_def
rw [c_def] at cOpt_in_arr
exact cOpt_in_arr
Proof state after:
no goals
Theorem: LRAT.DefaultFormula.ofArray_readyForRupAdd
Proof state before:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
b_eq_true : b = true
⊢ unit (i, b) ∈ (ofArray arr).toList
Tactic:
rw [isUnit_iff, DefaultClause.toList] at heq
Proof state after:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
modified_assignments_invariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : modified_assignments_invariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.data
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.clause = [(l, true)]
i_in_bounds : i.val < acc.size
l_in_bounds : l.val < acc.size
hsize : acc.size = n
ih : ∀ (i : PosFin n) (b : Bool), hasAssignment b acc[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
i_eq_l : i.val = l.val
h : hasAssignment b acc[l.val].addPosAssignment = true
b_eq_true : b = true
⊢ unit (i, b) ∈ (ofArray arr).toList