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Proof step 184 from proof putarray-addarray-01 (previous step)

i→n(i1 + i) = n + i→n(i), 0 ≤ i1, 0 ≤ i1 + i, 0 ≤ n→i(# vals) + i, 0 ≤ j, 0 ≤ i, i ≤ j, j ≤ n→i(# vals) + i, i1 < n→i(# vals), 0 < i + n→i(# vals) ⊦ vals = [], vals[i→n(i1)] = vals[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 183:
0 ≤ i, 0 ≤ j ⊦ i→n(i + j) = i→n(i) + i→n(j)

Rule argument

[speclemmaarg: 0 ≤ i, 0 ≤ j ,i→n(i + j) = i→n(i) + i→n(j) ,[j, i] → [i, i1] ,F ,intnat , ,add-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (i, i1)]]