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Proof step 72 from proof putarray-addarray-01 (previous step)

i→n(i2) = n + # vals, 0 < n→i(# vals) + i0, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i, 0 < i0, 0 ≤ i0 + i + n→i(# vals), 0 ≤ i0 + n→i(# vals), 0 ≤ i, i2 < n→i(# vals), 0 ≤ i2 + i, 0 ≤ i2, # vals ≤ i→n(i2) ⊦ vals = [], vals[i→n(i2)] = (mklist(initial_value(ty), i→n(i0))[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 71:
0 ≤ i ⊦ ((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i

Rule argument

[speclemmaarg: 0 ≤ i ,((* m)) ≤ i→n(i) ↔ n→i(m) ≤ i ,[i, m] → [i2, # vals] ,F ,intnat , ,num-i2n-le-02 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (i2, # vals)]]