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Proof step 103 from proof putarray-addarray-01 (previous step)

0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ sk = _length, ( r -- sk ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) ↔ r -- sk ∈ addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- sk]) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- sk])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[crewrite-arg: add-in-fskey , F , [st, vals, ty, sk, r] → [st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, sk, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, sk, r)]]