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Proof step 89 from proof putarray-addarray-01 (previous step)

sk = i1 ', 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 ≤ i1 ∧ i1 < 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])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ r -- j ' ∈ addarray(r, ty, vals, st) ↔ r -- j ' ∈ st ∨ 0 ≤ j ∧ j < n→i(# vals)
Proof step 88:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (r -- i1 ' ∈ addarray(r, ty, i0 + i + n→i(# vals), st) ∨ i ≤ i1 ∧ i1 < i + n→i(# vals) ↔ r -- i1 ' ∈ st ∨ ¬ i1 < 0 ∧ ¬ i + n→i(# vals) + i0 ≤ i1) ∧ (putArray(vals, r, i, addarray(r, ty, i0 + i + n→i(# vals), st))[r -- i1 ']) = (addarray(r, ty, mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)), st)[r -- i1 '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ 0 < i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ # mklist(val, n) = n], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ is_indexkey(i ')], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ _length ≠ i '])]]