simp
D : Type
I : Interpretation D
V : VarAssignment D
F : Formula
z : String
h1 : ¬occursFreeIn (free_ z) F
d : D
a1 : occursFreeIn (bound_ 0) F
⊢ d =
    if
        (if 0 < 0 then bound_ 0
          else if x : 0 - 0 < [free_ z].length then [free_ z][0 - 0] else bound_ (0 - 0 - [free_ z].length + 0)) =
          free_ z then
      d
    else
      V
        (if 0 < 0 then bound_ 0
        else if x : 0 - 0 < [free_ z].length then [free_ z][0 - 0] else bound_ (0 - 0 - [free_ z].length + 0))
no goals