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Proof step 136 from proof addarray-put-01 (previous step)

0 ≤ i0, is_indexkey(sk) ⊦ sk = 0 ', (addarray(r, ty, 1 + i0, st)[r -- sk]) = (addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = _length, sk = _type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 109:
⊦ is_indexkey(sk) ↔ (∃ i. sk = i ')
Proof step 135:
0 ≤ i0, ∃ i. sk = i ' ⊦ sk = 0 ', (addarray(r, ty, 1 + i0, st)[r -- sk]) = (addarray(r, ty, val ' + mklist(initial_value(ty), i→n(i0)), st)[r -- sk]), sk = _length, sk = _type

Rule argument

[speclemmaarg: ,is_indexkey(sk) ↔ (∃ i. sk = i ') ,[sk] → [sk] ,F ,storekey , ,ex-04 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk)]]