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Proof step 84 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 83:
⊦ i ≥ 0 → (((* i)) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m)

Rule argument

[speclemmaarg: ,i ≥ 0 → (((* i)) + n→i(n) ≤ n→i(m) ↔ i→n(i) + n ≤ m) ,[m, n, i] → [# vals0, # vals, i] ,F ,intnat , ,le-int-le-nat ]

Additional information

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