-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/Formula/Lemmas.lean
theorem readyForRupAdd_ofArray {n : Nat} (arr : Array (Option (DefaultClause n))) :
    ReadyForRupAdd (ofArray arr)

Proof state:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq✝ : c.isUnit = some (l, false)
heq : c.clause = [(l, false)]
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].addNegAssignment = true
b_eq_false : ¬b = true
i_eq_l : i = l
⊢ some { clause := [(l, false)], nodupkey := ⋯, nodup := ⋯ } ∈ arr.toList

Tactic:
have c_def : c = ⟨c.clause, c.nodupkey, c.nodup⟩ := rfl

Result:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq✝ : c.isUnit = some (l, false)
heq : c.clause = [(l, false)]
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].addNegAssignment = true
b_eq_false : ¬b = true
i_eq_l : i = l
c_def : c = { clause := c.clause, nodupkey := ⋯, nodup := ⋯ }
⊢ some { clause := [(l, false)], nodupkey := ⋯, nodup := ⋯ } ∈ arr.toList

Proof state:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq✝ : c.isUnit = some (l, false)
heq : c.clause = [(l, false)]
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].addNegAssignment = true
b_eq_false : ¬b = true
⊢ unit (i, b) ∈ (ofArray arr).toList

Tactic:
simp only [toList, ofArray, List.map, List.append_nil, List.mem_filterMap, id_eq, exists_eq_right]

Result:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq✝ : c.isUnit = some (l, false)
heq : c.clause = [(l, false)]
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].addNegAssignment = true
b_eq_false : ¬b = true
⊢ some (unit (i, b)) ∈ arr.toList

Proof state:
case left
n : Nat
arr : Array (Option (DefaultClause n))
⊢ (ofArray arr).rupUnits = #[]

Tactic:
simp only [ofArray]

Result:
no goals

Proof state:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
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_false : b = false
⊢ unit (i, b) ∈ (ofArray arr).toList

Tactic:
simp only [hasAssignment, b_eq_false, ite_false, hasNeg_addPos, reduceCtorEq] at h

Result:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
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
b_eq_false : b = false
h : acc[l.val].hasNegAssignment = true
⊢ unit (i, b) ∈ (ofArray arr).toList

Proof state:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
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_false : ¬b = true
⊢ unit (i, b) ∈ (ofArray arr).toList

Tactic:
simp only [Bool.not_eq_true] at b_eq_false

Result:
n : Nat
arr : Array (Option (DefaultClause n))
hsize✝¹ : (ofArray arr).assignments.size = n
ModifiedAssignmentsInvariant : Array Assignment → Prop :=
  fun assignments =>
    ∃ hsize, ∀ (i : PosFin n) (b : Bool), hasAssignment b assignments[i.val] = true → unit (i, b) ∈ (ofArray arr).toList
hb : ModifiedAssignmentsInvariant (mkArray n unassigned)
acc : Array Assignment
i : PosFin n
b : Bool
cOpt : Option (DefaultClause n)
c : DefaultClause n
cOpt_in_arr : some c ∈ arr.toList
hsize✝ : (ofArray_fold_fn acc (some c)).size = n
l : PosFin n
heq : c.isUnit = some (l, true)
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_false : b = false
⊢ unit (i, b) ∈ (ofArray arr).toList