Some more proofs.
consts exec :: ('a => 'v) => 'v list => (('a,'v) instr) list => 'v list
primrec
"exec s vs [] = vs"
"exec s vs (i#is) = (case i of
Const v => exec s (v#vs) is
| Load a => exec s ((s a)#vs) is
| Apply f => exec s ( (f (hd vs) (hd(tl vs)))#(tl(tl vs)) ) is)"