Theorem: LeanSAT.Model.PropForm.satisfies_biImpl' (LeanSAT/Model/PropForm.lean)

State before:
ν : Type u_1
τ : PropAssignment ν
x : ν
φ φ₁ φ₂ φ₃ : PropForm ν
⊢ τ ⊨ biImpl φ₁ φ₂ ↔ τ ⊨ φ₁ ∧ τ ⊨ φ₂ ∨ (fun M φ => ¬M ⊨ φ) τ φ₁ ∧ (fun M φ => ¬M ⊨ φ) τ φ₂
Tactic:
simp only [sEntails, satisfies, eval]
State after:
ν : Type u_1
τ : PropAssignment ν
x : ν
φ φ₁ φ₂ φ₃ : PropForm ν
⊢ decide (eval τ φ₁ = eval τ φ₂) = true ↔ eval τ φ₁ = true ∧ eval τ φ₂ = true ∨ ¬eval τ φ₁ = true ∧ ¬eval τ φ₂ = true

State before:
ν : Type u_1
τ : PropAssignment ν
x : ν
φ φ₁ φ₂ φ₃ : PropForm ν
⊢ decide (eval τ φ₁ = eval τ φ₂) = true ↔ eval τ φ₁ = true ∧ eval τ φ₂ = true ∨ ¬eval τ φ₁ = true ∧ ¬eval τ φ₂ = true
Tactic:
cases (eval τ φ₁) <;> aesop
State after:
no goals