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Proof step 9 from proof shift-1init (previous step)

⊦ r = r0, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))][r0 -- sk, val]) = addarray(r, ty, vals, st[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ addarray(r, ty, vals, st) = addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])
Proof step 8:
⊦ r = r0, addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))][r0 -- sk, val]) = addarray(r, vals, 0, st[r0 -- sk, val][r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])

Rule argument

[crewrite-arg: addarrayinit-def , F , [st, vals, ty, r] → [st[r0 -- sk, val], vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- sk, val], vals, ty, r)]]