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Proof step 91 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 = _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]), ¬ is_indexkey(sk) ∧ sk ≠ _type

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 90:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, is_indexkey(sk) ⊦ sk = _length, ( r -- sk ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ 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])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ i + j = j + i])]]