-- Mathlib/.lake/packages/lean4/src/lean/Std/Tactic/BVDecide/LRAT/Internal/LRATCheckerSound.lean
theorem lratCheckerSound [DecidableEq α] [Clause α β] [Entails α σ] [Formula α β σ] (f : σ)
    (f_readyForRupAdd : ReadyForRupAdd f) (f_readyForRatAdd : ReadyForRatAdd f)
    (prf : List (Action β α)) (prfWellFormed : ∀ a : Action β α, a ∈ prf → WellFormedAction a) :
    lratChecker f prf = success → Unsatisfiable α f

Proof state:
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝³ : DecidableEq α
inst✝² : Clause α β
inst✝¹ : Entails α σ
inst✝ : Formula α β σ
action : Action β α
restPrf : List (Action β α)
ih :
  ∀ (f : σ),
    ReadyForRupAdd f →
      ReadyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → WellFormedAction a) → lratChecker f restPrf = success → Unsatisfiable α f
f : σ
f_readyForRupAdd : ReadyForRupAdd f
f_readyForRatAdd : ReadyForRatAdd f
actionWellFormed : WellFormedAction action
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → WellFormedAction a
prf✝ : List (Action β α)
id : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
restPrf' : List (Action β α)
x✝ : σ × Bool
f' : σ
checkSuccess : Bool
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
hCheckSuccess : checkSuccess = true
f'_success : lratChecker f' restPrf = success
hprf : action = Action.addRat id c pivot rupHints ratHints ∧ restPrf = restPrf'
⊢ Unsatisfiable α f

Tactic:
simp only [WellFormedAction, hprf.1] at actionWellFormed

Result:
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝³ : DecidableEq α
inst✝² : Clause α β
inst✝¹ : Entails α σ
inst✝ : Formula α β σ
action : Action β α
restPrf : List (Action β α)
ih :
  ∀ (f : σ),
    ReadyForRupAdd f →
      ReadyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → WellFormedAction a) → lratChecker f restPrf = success → Unsatisfiable α f
f : σ
f_readyForRupAdd : ReadyForRupAdd f
f_readyForRatAdd : ReadyForRatAdd f
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → WellFormedAction a
prf✝ : List (Action β α)
id : Nat
c : β
pivot : Literal α
rupHints : Array Nat
ratHints : Array (Nat × Array Nat)
restPrf' : List (Action β α)
x✝ : σ × Bool
f' : σ
checkSuccess : Bool
heq : performRatAdd f c pivot rupHints ratHints = (f', true)
hCheckSuccess : checkSuccess = true
f'_success : lratChecker f' restPrf = success
hprf : action = Action.addRat id c pivot rupHints ratHints ∧ restPrf = restPrf'
actionWellFormed : Limplies α pivot c
⊢ Unsatisfiable α f

Proof state:
α : Type u_1
β : Type u_2
σ : Type u_3
inst✝³ : DecidableEq α
inst✝² : Clause α β
inst✝¹ : Entails α σ
inst✝ : Formula α β σ
action : Action β α
restPrf : List (Action β α)
ih :
  ∀ (f : σ),
    ReadyForRupAdd f →
      ReadyForRatAdd f →
        (∀ (a : Action β α), a ∈ restPrf → WellFormedAction a) → lratChecker f restPrf = success → Unsatisfiable α f
f : σ
f_readyForRupAdd : ReadyForRupAdd f
f_readyForRatAdd : ReadyForRatAdd f
actionWellFormed : WellFormedAction action
restPrfWellFormed : ∀ (a : Action β α), a ∈ restPrf → WellFormedAction a
prf✝ : List (Action β α)
id : Nat
rupHints : Array Nat
restPrf' : List (Action β α)
heq✝ : action :: restPrf = Action.addEmpty id rupHints :: restPrf'
rupAddSuccess : (performRupAdd f empty rupHints).snd = true
⊢ Unsatisfiable α f

Tactic:
exact addEmptyCaseSound f f_readyForRupAdd rupHints rupAddSuccess

Result:
no goals