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Proof step 60 from proof putarray-addarray-01 (previous step)

0 < i + n→i(# vals) + i0, 0 ≤ i1, i1 < i + n→i(# vals) + i0, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ 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)]

User applied rule cut formula

And obtained the following new goals

Proof step 59:
0 < i + n→i(# vals) + i0, 0 ≤ i1, i1 < i + n→i(# vals) + i0, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ i, n→i(# vals) + i ≤ i1 ⊦ i1 < i, initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)]

Rule argument

[fma-arg: i1 < i]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])], [EXTRAFMAS : (i1 < i)]]