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Proof step 199 from proof putarray-addarray-override (previous step)

fs ' = _length, # vals0 < i→n(i) + # vals, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0) ⊦ n→i(# vals0) = i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 198:
⊦ 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 : ⊦ m ≤ n → (n < m ↔ false)], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPSEQ : n ≤ # vals ⊦ # restn(n, vals) = # vals - n], [CSIMPSEQ : ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n)], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ 0 ≤ i → n→i(i→n(i)) = i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ n→i(m) = n→i(n) ↔ m = n])], [EXTRATERMS : (# vals0, # vals, i)]]