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Proof step 4 from proof add-at-gr (previous step)

0 ≤ i, ∀ st, ty, r, i, vals0. # vals0 < # [] → (n→i(# vals0) ≤ i → (addarray(r, ty, vals0, st)[r -- i ']) = st[r -- i ']) ⊦ (addarray(r, ty, [], st)[r -- i ']) = st[r -- i ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ addarray(r, ty, vals, st) = addarray(r, vals, 0, st[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals))])
Proof step 3:
⊦ addarray(r, [], i, st) = st

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ _length ≠ i '], [CSIMPSEQ : ⊦ _type ≠ i '])], [EXTRATERMS : (st, [], ty, r)]]