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Proof step 179 from proof putarray-addarray-01 (previous step)

i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < j, 0 < i, i0 < i, 0 < i + n→i(# vals), 0 ≤ i0, i0 < i + n→i(# vals), j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j, 0 ≤ n→i(# vals) + i, i0 < n→i(# vals) + i, 0 < j ⊦ (addarray(r, ty, j, st)[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 173:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)
Proof step 178:
i0 < j, 0 < i, i0 < i, 0 < i + n→i(# vals), 0 ≤ i0, i0 < i + n→i(# vals), j ≤ n→i(# vals) + i, i ≤ j, 0 ≤ i, 0 ≤ j, 0 ≤ n→i(# vals) + i, i0 < n→i(# vals) + i, 0 < j ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]