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Proof step 77 from proof putarray-addarray-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 69:
0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j)
Proof step 76:
0 ≤ i2 ∧ 0 ≤ i, i→n(i2) + i→n(i) = n + i→n(i), 0 ≤ i2, 0 ≤ i2 + i, i2 < n→i(# vals), 0 ≤ i, 0 ≤ i0 + n→i(# vals), 0 ≤ i0 + i + n→i(# vals), 0 < i0, 0 < n→i(# vals) + i, i2 < n→i(# vals) + i0, 0 < n→i(# vals) + i0 ⊦ vals = [], vals[i→n(i2)] = (vals + mklist(initial_value(ty), i→n(i0)))[n]

Rule argument

[speclemmaarg: 0 ≤ i, 0 ≤ j ,i→n(i + j) = i→n(i) + i→n(j) ,[j, i] → [i, i2] ,F ,intnat , ,add-01 ]

Additional information

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