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Proof step 11 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 7:
⊦ rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val])
Proof step 10:
r -- n→i(# vals0) ' ≠ r -- _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 -- n→i(# vals0) ', val][r -- _type, typeval(mkarraytype(ty))][r -- _length, intval(n→i(# vals0) + 1)])

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk, val0]) = (st[rk, val0][rk0, val]) ,[val0, rk, val, rk0, st] → [val, r -- n→i(# vals0) ', typeval(mkarraytype(ty)), r -- _type, addarray(r, vals0, 0, st)] ,F ,store ,javastore ,rew ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ _type ≠ i '])], [EXTRATERMS : (val, r -- n→i(# vals0) ', typeval(mkarraytype(ty)), r -- _type, addarray(r, vals0, 0, st))]]