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Proof step 115 from proof putarray-addarray-override (previous step)

0 < i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), # vals0 < i→n(i) + # vals, 0 < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), n→i(n) < n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)), 0 ≤ n→i(n) + i ⊦ (putArray(vals, r0, i, 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 114:
⊦ 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 ↔ ¬ i < j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ m ≤ n → (n < m ↔ false)])], [EXTRATERMS : (# vals0, # vals, i)]]