case intro h1_1_left h1_1_right =>
  contradiction
D : Type
I : Interpretation D
E : Env
v t : VarName
F F' : Formula
h1_x : VarName
h1_phi : Formula
h1_v h1_t : VarName
h1_phi' : Formula
h1_2 : ¬h1_x = h1_t
a✝ : IsSub h1_phi h1_v h1_t h1_phi'
V : VarAssignment D
d : D
h1_ih :
  Holds D I (Function.updateITE (Function.updateITE V h1_x d) h1_v (Function.updateITE V h1_x d h1_t)) E h1_phi ↔
    Holds D I (Function.updateITE V h1_x d) E h1_phi'
c1 : isFreeIn h1_x h1_phi
c3 : h1_v = h1_x
h1_1_left : ¬h1_v = h1_x
h1_1_right : isFreeIn h1_v h1_phi
⊢ d = V h1_t
no goals