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Proof step 99 from proof putarray-addarray-override (previous step)

# vals0 < i→n(i) + # vals, i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) < n→i(# vals0), n→i(# vals) + i < n→i(# vals0), i0 < n→i(# vals0), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0, n→i(# vals) + i ≤ i0, 0 ≤ i0 ⊦ vals0 = [], vals0[i→n(i0)] = st[r0 -- i0 ']

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 98:
0 ≤ i ⊦ ((* i)) ≤ n→i(n) ↔ i→n(i) ≤ n

Rule argument

[speclemmaarg: 0 ≤ i ,((* i)) ≤ n→i(n) ↔ i→n(i) ≤ n ,[n, i] → [# vals0, i + n→i(# vals)] ,F ,intnat , ,num-n2i-ls-06 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)], [CSIMPSEQ : ⊦ m + n = n + m], [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 : ⊦ i < 0 ∧ 0 ≤ j → i ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i < 0 ∧ 0 ≤ j → i < j], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (# vals0, i + n→i(# vals))]]