induction as
a : Program
as : List Program
c : Program
P : LoadFormula
⊢ (~'⌊a⌋⌊⌊as ++ [c]⌋⌋P) = ~'⌊a⌋⌊⌊as⌋⌋⌊c⌋P
case nil
a c : Program
P : LoadFormula
⊢ (~'⌊a⌋⌊⌊[] ++ [c]⌋⌋P) = ~'⌊a⌋⌊⌊[]⌋⌋⌊c⌋P

case cons
a c : Program
P : LoadFormula
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