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Proof step 62 from proof putarray-addarray-01 (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 35:
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 ⊦ ¬ i1 < i, initial_value(ty) = (mklist(initial_value(ty), i→n(i)) + vals + mklist(initial_value(ty), i→n(i0)))[i→n(i1)]
Proof step 61:
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 ⊦ ¬ 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)]

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]