Theorem: LRAT.DefaultFormula.deleteOne_preserves_strong_assignments_invariant
Proof state before:
n : Nat
f : DefaultFormula n
id : Nat
hsize : f.assignments.size = n
hf : ∀ (i : PosFin n) (b : Bool), hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
hsize' : (f.deleteOne id).assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.deleteOne id).assignments[i.val] = true
i_in_bounds : i.val < f.assignments.size
c : DefaultClause n
heq : f.clauses[id]! = some c
x✝² : Option (DefaultClause n)
val✝ : DefaultClause n
x✝¹ :
  ∀ (l : Literal (PosFin n)) (nodupkey : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l])
    (nodup : [l].Nodup), val✝ = { clause := [l], nodupkey := nodupkey, nodup := nodup } → False
heq✝ : some c = some val✝
x✝ : Option (DefaultClause n)
l : Literal (PosFin n)
nodupkey✝ : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l]
nodup✝ : [l].Nodup
heq2 : c = { clause := [l], nodupkey := nodupkey✝, nodup := nodup✝ }
hl : ¬l = (l.fst, false) ∧ ¬l = (l.fst, true)
⊢ { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
      assignments := f.assignments.modify l.fst.val (removeAssignment l.snd) } =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }
Tactic:
by_cases hl2 : l.2
Proof state after:
case pos
n : Nat
f : DefaultFormula n
id : Nat
hsize : f.assignments.size = n
hf : ∀ (i : PosFin n) (b : Bool), hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
hsize' : (f.deleteOne id).assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.deleteOne id).assignments[i.val] = true
i_in_bounds : i.val < f.assignments.size
c : DefaultClause n
heq : f.clauses[id]! = some c
x✝² : Option (DefaultClause n)
val✝ : DefaultClause n
x✝¹ :
  ∀ (l : Literal (PosFin n)) (nodupkey : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l])
    (nodup : [l].Nodup), val✝ = { clause := [l], nodupkey := nodupkey, nodup := nodup } → False
heq✝ : some c = some val✝
x✝ : Option (DefaultClause n)
l : Literal (PosFin n)
nodupkey✝ : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l]
nodup✝ : [l].Nodup
heq2 : c = { clause := [l], nodupkey := nodupkey✝, nodup := nodup✝ }
hl : ¬l = (l.fst, false) ∧ ¬l = (l.fst, true)
hl2 : l.snd = true
⊢ { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
      assignments := f.assignments.modify l.fst.val (removeAssignment l.snd) } =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }

case neg
n : Nat
f : DefaultFormula n
id : Nat
hsize : f.assignments.size = n
hf : ∀ (i : PosFin n) (b : Bool), hasAssignment b f.assignments[i.val] = true → unit (i, b) ∈ f.toList
hsize' : (f.deleteOne id).assignments.size = n
i : PosFin n
b : Bool
hb : hasAssignment b (f.deleteOne id).assignments[i.val] = true
i_in_bounds : i.val < f.assignments.size
c : DefaultClause n
heq : f.clauses[id]! = some c
x✝² : Option (DefaultClause n)
val✝ : DefaultClause n
x✝¹ :
  ∀ (l : Literal (PosFin n)) (nodupkey : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l])
    (nodup : [l].Nodup), val✝ = { clause := [l], nodupkey := nodupkey, nodup := nodup } → False
heq✝ : some c = some val✝
x✝ : Option (DefaultClause n)
l : Literal (PosFin n)
nodupkey✝ : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l]
nodup✝ : [l].Nodup
heq2 : c = { clause := [l], nodupkey := nodupkey✝, nodup := nodup✝ }
hl : ¬l = (l.fst, false) ∧ ¬l = (l.fst, true)
hl2 : ¬l.snd = true
⊢ { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
      assignments := f.assignments.modify l.fst.val (removeAssignment l.snd) } =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }