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Proof step 13 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 -- _type, typeval(mkarraytype(ty))])[r -- n→i(# vals0) ', val][r -- _length, intval(n→i(# vals0) + 1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_fskey(sk) → addarray(r, vals, i, st[r0 -- sk, val]) = (addarray(r, vals, i, st)[r0 -- sk, val])
Proof step 12:
is_fskey(_type) ⊦ (addarray(r, vals0 + val ', 0, st)[r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals0) + 1)]) = (addarray(r, vals0, 0, st)[r -- _type, typeval(mkarraytype(ty))][r -- n→i(# vals0) ', val][r -- _length, intval(n→i(# vals0) + 1)])

Rule argument

[crewrite-arg: init-switch , F , [val, sk, r0, st, i, vals, r] → [typeval(mkarraytype(ty)), _type, r, st, 0, vals0, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(_type)])], [EXTRATERMS : (typeval(mkarraytype(ty)), _type, r, st, 0, vals0, r)]]