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
hl :
  ∀ (x : PosFin n),
    ¬c = { clause := [(x, false)], nodupkey := ⋯, nodup := ⋯ } ∧
      ¬c = { clause := [(x, true)], nodupkey := ⋯, nodup := ⋯ }
x✝¹ : Option (DefaultClause n)
val✝ : DefaultClause n
x✝ :
  ∀ (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✝
⊢ (match f.clauses[id]! with
    | none => { clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }
    | some { clause := [l], nodupkey := nodupkey, nodup := nodup } =>
      { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments.modify l.fst.val (removeAssignment l.snd) }
    | some val =>
      { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits,
        assignments := f.assignments }) =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }
Tactic:
split
Proof state after:
case h_1
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
hl :
  ∀ (x : PosFin n),
    ¬c = { clause := [(x, false)], nodupkey := ⋯, nodup := ⋯ } ∧
      ¬c = { clause := [(x, true)], nodupkey := ⋯, nodup := ⋯ }
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✝¹ : some c = some val✝
x✝ : Option (DefaultClause n)
heq✝ : f.clauses[id]! = none
⊢ { clauses := f.clauses, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments } =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }

case h_2
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
hl :
  ∀ (x : PosFin n),
    ¬c = { clause := [(x, false)], nodupkey := ⋯, nodup := ⋯ } ∧
      ¬c = { clause := [(x, true)], nodupkey := ⋯, nodup := ⋯ }
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✝¹ : some c = some val✝
x✝ : Option (DefaultClause n)
l✝ : Literal (PosFin n)
nodupkey✝ : ∀ (l : PosFin n), ¬(l, true) ∈ [l✝] ∨ ¬(l, false) ∈ [l✝]
nodup✝ : [l✝].Nodup
heq✝ : f.clauses[id]! = some { clause := [l✝], nodupkey := nodupkey✝, nodup := nodup✝ }
⊢ { 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 h_3
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
hl :
  ∀ (x : PosFin n),
    ¬c = { clause := [(x, false)], nodupkey := ⋯, nodup := ⋯ } ∧
      ¬c = { clause := [(x, true)], nodupkey := ⋯, nodup := ⋯ }
x✝³ : Option (DefaultClause n)
val✝¹ : DefaultClause n
x✝² :
  ∀ (l : Literal (PosFin n)) (nodupkey : ∀ (l_1 : PosFin n), ¬(l_1, true) ∈ [l] ∨ ¬(l_1, false) ∈ [l])
    (nodup : [l].Nodup), val✝¹ = { clause := [l], nodupkey := nodupkey, nodup := nodup } → False
heq✝¹ : some c = some val✝¹
x✝¹ : Option (DefaultClause n)
val✝ : DefaultClause n
x✝ :
  ∀ (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✝ : f.clauses[id]! = some val✝
⊢ { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments } =
    { clauses := f.clauses.set! id none, rupUnits := f.rupUnits, ratUnits := f.ratUnits, assignments := f.assignments }