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Proof step 63 from proof putarray-addarray-01 (previous step)

0 ≤ i1 ∧ i1 < n→i(# (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))), i1 < i ∨ n→i(# vals) + i ≤ i1, 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0 ⊦ (addarray(r, ty, i0 + i + n→i(# vals), st)[r -- i1 ']) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)], ¬ i1 < i ∧ ¬ n→i(# vals) + i ≤ i1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
⊦ 0 ≤ j ∧ j < i → (addarray(r, ty, i, st)[r -- j ']) = initial_value(ty)
Proof step 62:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, i1 < i + n→i(# vals) + i0, 0 ≤ i1, 0 < i + n→i(# vals) + i0, i1 < i ∨ n→i(# vals) + i ≤ i1 ⊦ initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)], ¬ i1 < i ∧ ¬ n→i(# vals) + i ≤ i1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [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])]]