Theorem: LO.Modal.Standard.provable_efq_of_provable_S4.case_imply₁ (Logic/Modal/Standard/Kripke/ModalCompanion.lean)

State before:
α : Type u_1
inst✝³ : DecidableEq α
inst✝² : Inhabited α
inst✝¹ : Encodable α
i𝓓 : Superintuitionistic.DeductionParameter α
m𝓓 : DeductionParameter α
p q r : Superintuitionistic.Formula α
inst✝ : K4 m𝓓
⊢ m𝓓 ⊢! (p ⟶ q ⟶ p)ᵍ
Tactic:
simp only [GoedelTranslation.imp_def]
State after:
α : Type u_1
inst✝³ : DecidableEq α
inst✝² : Inhabited α
inst✝¹ : Encodable α
i𝓓 : Superintuitionistic.DeductionParameter α
m𝓓 : DeductionParameter α
p q r : Superintuitionistic.Formula α
inst✝ : K4 m𝓓
⊢ m𝓓 ⊢! □(pᵍ ⟶ □(qᵍ ⟶ pᵍ))

State before:
α : Type u_1
inst✝³ : DecidableEq α
inst✝² : Inhabited α
inst✝¹ : Encodable α
i𝓓 : Superintuitionistic.DeductionParameter α
m𝓓 : DeductionParameter α
p q r : Superintuitionistic.Formula α
inst✝ : K4 m𝓓
⊢ m𝓓 ⊢! □(pᵍ ⟶ □(qᵍ ⟶ pᵍ))
Tactic:
exact nec! $ imp_trans! axiomTc_GTranslate! $ axiomK'! $ nec! $ imply₁!
State after:
no goals