induction as
a : Program
as : List Program
c : Program
P : Formula
⊢ (~⌈a⌉⌈⌈as ++ [c]⌉⌉P) = (~⌈a⌉⌈⌈as⌉⌉⌈c⌉P)
case nil
a c : Program
P : Formula
⊢ (~⌈a⌉⌈⌈[] ++ [c]⌉⌉P) = (~⌈a⌉⌈⌈[]⌉⌉⌈c⌉P)

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)