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Proof step 10 from proof putarray-add-butlast (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_fskey(sk) → addarray(r, vals, i, st[r0 -- sk, val]) = (addarray(r, vals, i, st)[r0 -- sk, val])

Rule argument

[crewrite-arg: init-switch , F , [val, sk, r0, st, i, vals, r] → [intval(n→i(# vals) + 1), _length, r, st[r -- _type, typeval(mkarraytype(ty))], 0, vals, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(_length)], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (intval(n→i(# vals) + 1), _length, r, st[r -- _type, typeval(mkarraytype(ty))], 0, vals, r)]]