internlm/Lean-Github huggingface dataset:
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res_unsat :
  unsatisfiable α
    (match Action.addRup id✝ c rupHints with
      | Action.addEmpty id rupHints =>
        match performRupAdd f empty rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, success) else (f, rup_failure)
      | Action.addRup id c rupHints =>
        match performRupAdd f c rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.addRat id c pivot rupHints ratHints =>
        match performRatAdd f c pivot rupHints ratHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.del ids => (Formula.delete f ids, out_of_proof)).fst
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
heq : performRupAdd f c rupHints = (f', true)
f_liff_f' : liff α f f'
⊢ unsatisfiable α f
Tactic:
simp only [performRupAdd_success, ite_true] at incrementalChecker_res_unsat
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
heq : performRupAdd f c rupHints = (f', true)
f_liff_f' : liff α f f'
incrementalChecker_res_unsat : unsatisfiable α (performRupAdd f c rupHints).fst
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
heq : performRupAdd f c rupHints = (f', true)
f_liff_f' : liff α f f'
incrementalChecker_res_unsat : unsatisfiable α (performRupAdd f c rupHints).fst
⊢ unsatisfiable α f
Tactic:
rw [liff_unsat f f' f_liff_f']
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
heq : performRupAdd f c rupHints = (f', true)
f_liff_f' : liff α f f'
incrementalChecker_res_unsat : unsatisfiable α (performRupAdd f c rupHints).fst
⊢ unsatisfiable α f'
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
heq : performRupAdd f c rupHints = (f', true)
f_liff_f' : liff α f f'
incrementalChecker_res_unsat : unsatisfiable α (performRupAdd f c rupHints).fst
⊢ unsatisfiable α f'
Tactic:
exact incrementalChecker_res_unsat
Proof state after:
no goals
Theorem: incrementalLRATCheckerSound
Proof state before:
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f (Action.addRup id✝ c rupHints)).fst
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = true
f' : σ := (performRupAdd f c rupHints).fst
⊢ performRupAdd f c rupHints = (f', true)
Tactic:
rw [← performRupAdd_success]
Proof state after:
no goals
Theorem: incrementalLRATCheckerSound
Proof state before:
case neg
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f (Action.addRup id✝ c rupHints)).fst
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : ¬(performRupAdd f c rupHints).snd = true
⊢ unsatisfiable α f
Tactic:
simp only [Bool.not_eq_true] at performRupAdd_success
Proof state after:
case neg
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f (Action.addRup id✝ c rupHints)).fst
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = false
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case neg
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
rupHints : Array Nat
aWellFormed : wellFormedAction (Action.addRup id✝ c rupHints)
incrementalChecker_res_unsat : unsatisfiable α (incrementalLRATChecker f (Action.addRup id✝ c rupHints)).fst
incrementalChecker_res :
  (if (performRupAdd f c rupHints).snd = true then ((performRupAdd f c rupHints).fst, out_of_proof)
      else ((performRupAdd f c rupHints).fst, rup_failure)).snd =
    out_of_proof
performRupAdd_success : (performRupAdd f c rupHints).snd = false
⊢ unsatisfiable α f
Tactic:
simp only [performRupAdd_success, ite_false] at incrementalChecker_res
Proof state after:
no goals
Theorem: incrementalLRATCheckerSound
Proof state before:
case right.h_3
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c✝ : β
pivot✝ : Literal α
rupHints✝ : Array Nat
ratHints✝ : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c✝ pivot✝ rupHints✝ ratHints✝)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c✝ pivot✝ rupHints✝ ratHints✝)).fst
incrementalChecker_res :
  (if (performRatAdd f c✝ pivot✝ rupHints✝ ratHints✝).snd = true then
        ((performRatAdd f c✝ pivot✝ rupHints✝ ratHints✝).fst, out_of_proof)
      else ((performRatAdd f c✝ pivot✝ rupHints✝ ratHints✝).fst, rup_failure)).snd =
    out_of_proof
⊢ unsatisfiable α f
Tactic:
next c pivot rupHints ratHints =>
by_cases performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).2
. let f' := (performRatAdd f c pivot rupHints ratHints).1
  have heq : performRatAdd f c pivot rupHints ratHints = (f', true) := by rw [← performRatAdd_success]
  simp only [wellFormedAction, limplies_iff_mem] at aWellFormed
  unfold incrementalLRATChecker at incrementalChecker_res_unsat
  simp only [performRatAdd_success, ite_true] at incrementalChecker_res_unsat
  have h := ratAdd_sound f c pivot rupHints ratHints f' f_readyForRatAdd aWellFormed heq
  rw [equisat] at h
  rw [h]
  exact incrementalChecker_res_unsat
. simp only [Bool.not_eq_true] at performRatAdd_success
  simp only [performRatAdd_success, ite_false] at incrementalChecker_res
Proof state after:
no goals
Theorem: incrementalLRATCheckerSound
Proof state before:
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
⊢ unsatisfiable α f
Tactic:
by_cases performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).2
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
⊢ unsatisfiable α f

case neg
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : ¬(performRatAdd f c pivot rupHints ratHints).snd = true
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case neg
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : ¬(performRatAdd f c pivot rupHints ratHints).snd = true
⊢ unsatisfiable α f
Tactic:
. simp only [Bool.not_eq_true] at performRatAdd_success
  simp only [performRatAdd_success, ite_false] at incrementalChecker_res
Proof state after:
no goals
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
⊢ unsatisfiable α f
Tactic:
let f' := (performRatAdd f c pivot rupHints ratHints).1
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
⊢ unsatisfiable α f
Tactic:
have heq : performRatAdd f c pivot rupHints ratHints = (f', true) := by rw [← performRatAdd_success]
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
aWellFormed : wellFormedAction (Action.addRat id✝ c pivot rupHints ratHints)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
⊢ unsatisfiable α f
Tactic:
simp only [wellFormedAction, limplies_iff_mem] at aWellFormed
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
aWellFormed : pivot ∈ Clause.toList c
⊢ unsatisfiable α f
Theorem: incrementalLRATCheckerSound
Proof state before:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
incrementalChecker_res_unsat :
  unsatisfiable α (incrementalLRATChecker f (Action.addRat id✝ c pivot rupHints ratHints)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
aWellFormed : pivot ∈ Clause.toList c
⊢ unsatisfiable α f
Tactic:
unfold incrementalLRATChecker at incrementalChecker_res_unsat
Proof state after:
case pos
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝² : DecidableEq α
inst✝¹ : Clause α β
inst✝ : Formula α β σ
f : σ
f_readyForRupAdd : readyForRupAdd f
f_readyForRatAdd : readyForRatAdd f
action✝ : Action β α
id✝ : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
incrementalChecker_res_unsat :
  unsatisfiable α
    (match Action.addRat id✝ c pivot rupHints ratHints with
      | Action.addEmpty id rupHints =>
        match performRupAdd f empty rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, success) else (f, rup_failure)
      | Action.addRup id c rupHints =>
        match performRupAdd f c rupHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.addRat id c pivot rupHints ratHints =>
        match performRatAdd f c pivot rupHints ratHints with
        | (f, checkSuccess) => if checkSuccess = true then (f, out_of_proof) else (f, rup_failure)
      | Action.del ids => (Formula.delete f ids, out_of_proof)).fst
incrementalChecker_res :
  (if (performRatAdd f c pivot rupHints ratHints).snd = true then
        ((performRatAdd f c pivot rupHints ratHints).fst, out_of_proof)
      else ((performRatAdd f c pivot rupHints ratHints).fst, rup_failure)).snd =
    out_of_proof
performRatAdd_success : (performRatAdd f c pivot rupHints ratHints).snd = true
f' : σ := (performRatAdd f c pivot rupHints ratHints).fst
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
aWellFormed : pivot ∈ Clause.toList c
⊢ unsatisfiable α f