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Proof step 101 from proof putarray-addarray-01 (previous step)

is_fskey(sk), 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ sk = _type, sk = _length, (is_indexkey(sk) ∧ i ≤ sk .index ∧ sk .index < i + n→i(# vals) → r -- sk ∈ st) ∧ 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

Proof step 100:
⊦ is_fskey(sk) ∧ sk ≠ _length ∧ sk ≠ _type → (addarray(r, ty, vals, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[crewrite-arg: add-at-04 , F , [sk, r0, st, vals, ty, r] → [sk, r, st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)])], [EXTRATERMS : (sk, r, st, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), ty, r)]]