congr! 1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
a✝¹ : IsConv E h2_phi h2_phi'
a✝ : IsConv E h2_psi h2_psi'
h2_ih_1 : ∀ (V : Valuation D), Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'
h2_ih_2 : ∀ (V : Valuation D), Holds D I V M E h2_psi ↔ Holds D I V M E h2_psi'
V : Valuation D
⊢ Holds D I V M E h2_phi → Holds D I V M E h2_psi ↔ Holds D I V M E h2_phi' → Holds D I V M E h2_psi'
case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
a✝¹ : IsConv E h2_phi h2_phi'
a✝ : IsConv E h2_psi h2_psi'
h2_ih_1 : ∀ (V : Valuation D), Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'
h2_ih_2 : ∀ (V : Valuation D), Holds D I V M E h2_psi ↔ Holds D I V M E h2_psi'
V : Valuation D
⊢ Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'

case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
a✝² : IsConv E h2_phi h2_phi'
a✝¹ : IsConv E h2_psi h2_psi'
h2_ih_1 : ∀ (V : Valuation D), Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi'
h2_ih_2 : ∀ (V : Valuation D), Holds D I V M E h2_psi ↔ Holds D I V M E h2_psi'
V : Valuation D
a✝ : Holds D I V M E h2_phi'
⊢ Holds D I V M E h2_psi ↔ Holds D I V M E h2_psi'