case conv_trans h2_phi h2_phi' h2_phi'' _ _ h2_ih_1 h2_ih_2 =>
  trans Holds D I V M E h2_phi'
  exact h2_ih_1 V
  exact h2_ih_2 V
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
a✝¹ : IsConv E h2_phi h2_phi'
a✝ : IsConv E h2_phi' h2_phi''
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_phi' ↔ Holds D I V M E h2_phi''
V : Valuation D
⊢ Holds D I V M E h2_phi ↔ Holds D I V M E h2_phi''
no goals