simp at *
case cons
a c : Program
P : Formula
head✝ : Program
tail✝ : List Program
tail_ih✝ : (~⌈a⌉⌈⌈tail✝ ++ [c]⌉⌉P) = (~⌈a⌉⌈⌈tail✝⌉⌉⌈c⌉P)
⊢ (~⌈a⌉⌈⌈head✝ :: tail✝ ++ [c]⌉⌉P) = (~⌈a⌉⌈⌈head✝ :: tail✝⌉⌉⌈c⌉P)
case cons
a c : Program
P : Formula
head✝ : Program
tail✝ : List Program
tail_ih✝ : (⌈⌈tail✝ ++ [c]⌉⌉P) = ⌈⌈tail✝⌉⌉⌈c⌉P
⊢ (⌈⌈tail✝ ++ [c]⌉⌉P) = ⌈⌈tail✝⌉⌉⌈c⌉P