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Proof step 9 from proof add-lastrec (previous step)

⊦ (addarray(r, vals0 + val ', 0, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals0) + 1)]) = (addarray(r, vals0, 0, st)[r -- n→i(# vals0) ', val][r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals0) + 1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ addarray(r, vals + val ', i, st) = (addarray(r, vals, i, st)[r -- (i + n→i(# vals)) ', val])

Rule argument

[crewrite-arg: init-last , F , [st, i, val, vals, r] → [st, 0, val, vals0, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRATERMS : (st, 0, val, vals0, r)]]