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Proof step 49 from proof putarray-addarray-01 (previous step)

0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, n→i(n) < n→i(# vals) + i0, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0, # vals ≤ n, 0 ≤ i + n→i(n) ⊦ 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 40:
⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0
Proof step 48:
0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, n→i(n) < n→i(# vals) + i0, 0 < i + n→i(# vals) + i0, 0 < n→i(# vals) + i0, # vals ≤ n, 0 - n→i(n) ≤ i ⊦ initial_value(ty) = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

[speclemmaarg: ,((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0 ,[j0, i0, j] → [n→i(n), i, 0] ,F ,int-abs , ,numle-02 ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n→i(n), i, 0)]]