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Proof step 128 from proof putarray-addarray-override (previous step)

0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n < # vals0, 0 ≤ n→i(n) + i, # vals ≤ n, n→i(# vals0) ≤ n→i(n) + i ⊦ vals0 = [], (addarray(r0, ty, vals0, st)[r0 -- (n→i(n) + i) ']) = (vals + restn(i→n(i) + # vals, vals0))[n]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 127:
0 ≤ i ⊦ n→i(n) ≤ ((* i)) ↔ n ≤ i→n(i)

Rule argument

[speclemmaarg: 0 ≤ i ,n→i(n) ≤ ((* i)) ↔ n ≤ i→n(i) ,[i, n] → [n→i(n) + i, # vals0] ,F ,intnat , ,num-n2i-ls-04 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + n→i(n)) = i→n(i) + n], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)])], [EXTRATERMS : (n→i(n) + i, # vals0)]]