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Proof step 193 from proof putarray-addarray-01 (previous step)

0 ≤ i0 ∧ i0 < n→i(# (mklist(initial_value(ty), i→n(i)) + vals)), 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i ⊦ (putArray(vals, r, i, 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 192:
0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i0 < i + n→i(# vals), 0 ≤ i0, 0 < i + n→i(# vals) ⊦ (putArray(vals, r, i, addarray(r, ty, j, st))[r -- i0 ']) = (mklist(initial_value(ty), i→n(i)) + vals)[i→n(i0)]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [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])]]