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Proof step 12 from proof add-at-gr (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ vals ≠ [] → addarray(r, ty, vals, st) = (addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))])
Proof step 5:
¬ vals ≠ [], n→i(# vals) ≤ i, ∀ st, ty, r, i, vals0. # vals0 < # vals → (n→i(# vals0) ≤ i → (addarray(r, ty, vals0, st)[r -- i ']) = st[r -- i ']) ⊦ (addarray(r, ty, vals, st)[r -- i ']) = st[r -- i ']
Proof step 11:
vals ≠ [], n→i(# vals) ≤ i, ∀ st, ty, r, i, vals0. # vals0 < # vals → (n→i(# vals0) ≤ i → (addarray(r, ty, vals0, st)[r -- i ']) = st[r -- i ']) ⊦ (addarray(r, ty, vals .butlast, st)[r -- n→i((# vals) -1) ', vals .last][r -- _length, intval(n→i(# vals))][r -- i ']) = st[r -- i ']

Rule argument

[crewrite-arg: add-lastrec, F, [st, vals, ty, r] → [st, vals, ty, r]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, vals, ty, r)]]