Theorem: LO.Propositional.Superintuitionistic.Formula.Kripke.ValidOnFrame.disj₁ (Logic/Propositional/Superintuitionistic/Kripke/Semantics.lean)

State before:
α : Type u_1
inst✝ : Inhabited α
F : Frame' α
p q r : Formula α
⊢ F ⊧ p ⟶ p ⋎ q
Tactic:
simp_all only [ValidOnFrame.models_iff, ValidOnFrame, ValidOnModel.iff_models]
State after:
α : Type u_1
inst✝ : Inhabited α
F : Frame' α
p q r : Formula α
⊢ ∀ (V : Valuation F.World α) (h : ∀ {w₁ w₂ : F.World}, w₁ ≺ w₂ → ∀ {a : α}, V w₁ a → V w₂ a),
    ValidOnModel { Frame := F, Valuation := V, hereditary := h } (p ⟶ p ⋎ q)

State before:
α : Type u_1
inst✝ : Inhabited α
F : Frame' α
p q r : Formula α
⊢ ∀ (V : Valuation F.World α) (h : ∀ {w₁ w₂ : F.World}, w₁ ≺ w₂ → ∀ {a : α}, V w₁ a → V w₂ a),
    ValidOnModel { Frame := F, Valuation := V, hereditary := h } (p ⟶ p ⋎ q)
Tactic:
intros
State after:
α : Type u_1
inst✝ : Inhabited α
F : Frame' α
p q r : Formula α
V✝ : Valuation F.World α
h✝ : ∀ {w₁ w₂ : F.World}, w₁ ≺ w₂ → ∀ {a : α}, V✝ w₁ a → V✝ w₂ a
⊢ ValidOnModel { Frame := F, Valuation := V✝, hereditary := h✝ } (p ⟶ p ⋎ q)

State before:
α : Type u_1
inst✝ : Inhabited α
F : Frame' α
p q r : Formula α
V✝ : Valuation F.World α
h✝ : ∀ {w₁ w₂ : F.World}, w₁ ≺ w₂ → ∀ {a : α}, V✝ w₁ a → V✝ w₂ a
⊢ ValidOnModel { Frame := F, Valuation := V✝, hereditary := h✝ } (p ⟶ p ⋎ q)
Tactic:
apply ValidOnModel.disj₁
State after:
no goals