have IH := substitutionLemma σ φ M w
σ : Substitution
W : Type
M : KripkeModel W
w : W
φ : Formula
⊢ (M, w)⊨subst_in_F σ (~φ) ↔ (subst_in_model σ M, w)⊨(~φ)
σ : Substitution
W : Type
M : KripkeModel W
w : W
φ : Formula
IH : (M, w)⊨subst_in_F σ φ ↔ (subst_in_model σ M, w)⊨φ
⊢ (M, w)⊨subst_in_F σ (~φ) ↔ (subst_in_model σ M, w)⊨(~φ)