ext v
case a.e_a
ν : Type u_1
inst✝ : DecidableEq ν
φ✝ φ₁ φ₂ : PropForm ν
v✝ : ν
ψ ψ₁ ψ₂ φ : PropForm ν
v : ν
τ : PropAssignment ν
⊢ PropAssignment.subst (fun x => ⟦if x = v then ψ else var x⟧) τ = PropAssignment.set τ v (decide (τ ⊨ ψ))
case a.e_a.h
ν : Type u_1
inst✝ : DecidableEq ν
φ✝ φ₁ φ₂ : PropForm ν
v✝¹ : ν
ψ ψ₁ ψ₂ φ : PropForm ν
v✝ : ν
τ : PropAssignment ν
v : ν
⊢ PropAssignment.subst (fun x => ⟦if x = v✝ then ψ else var x⟧) τ v = PropAssignment.set τ v✝ (decide (τ ⊨ ψ)) v