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Proof step 54 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ i + ((* j)) ≤ ((* j0)) ↔ i ≤ j0 - j
Proof step 53:
i→n(i1) = n + i→n(i), n→i(# vals) ≤ i1 - i, 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, 0 < n→i(# vals) + i0, i ≤ i1 ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

[speclemmaarg: ,i + ((* j)) ≤ ((* j0)) ↔ i ≤ j0 - j ,[j0, j, i] → [i1, i, n→i(# vals)] ,F ,int-abs , ,numle-03 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i1, i, n→i(# vals))]]