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

case cons
bs : List Program
P : Formula
head✝ : Program
tail✝ : List Program
tail_ih✝ : (⌈⌈tail✝ ++ bs⌉⌉P) = ⌈⌈tail✝⌉⌉⌈⌈bs⌉⌉P
⊢ (⌈⌈head✝ :: tail✝ ++ bs⌉⌉P) = ⌈⌈head✝ :: tail✝⌉⌉⌈⌈bs⌉⌉P