apply ih
ν : Type u_1
inst✝¹ inst✝ : DecidableEq ν
τ' : PropAssignment ν
φ : PropFun ν
x : ν
vs : Finset ν
hx : x ∉ vs
ih : ∀ (τ : PropAssignment ν), PropAssignment.setMany τ vs τ' ⊨ φ ↔ PropAssignment.setMany τ (vs ∩ semVars φ) τ' ⊨ φ
τ : PropAssignment ν
h : x ∈ semVars φ
⊢ PropAssignment.setMany (PropAssignment.set τ x (τ' x)) vs τ' ⊨ φ ↔
    PropAssignment.setMany (PropAssignment.set τ x (τ' x)) (vs ∩ semVars φ) τ' ⊨ φ
no goals