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Proof step 139 from proof putarray-addarray-override (previous step)

(n→i(n0) + n→i(# vals)) + i < n→i(# vals0), 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n0 + # vals < # vals0, 0 ≤ (n→i(n0) + n→i(# vals)) + i ⊦ vals0 = [], vals0[i→n(i) + n0 + # vals] = (restn(i→n(i) + # vals, vals0)[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 131:
⊦ i ≥ 0 → (((* i)) + n→i(n) < n→i(m) ↔ i→n(i) + n < m)
Proof step 138:
i + n→i(# vals) ≥ 0, i→n(i + n→i(# vals)) + n0 < # vals0, 0 ≤ i, i→n(i) < # vals0, i→n(i) + # vals ≤ # vals0, i→n(i) + n0 + # vals < # vals0, 0 ≤ (n→i(n0) + n→i(# vals)) + i ⊦ vals0 = [], vals0[i→n(i) + n0 + # vals] = (restn(i→n(i) + # vals, vals0)[n0])

Rule argument

[speclemmaarg: ,i ≥ 0 → (((* i)) + n→i(n) < n→i(m) ↔ i→n(i) + n < m) ,[m, i, n] → [# vals0, i + n→i(# vals), n0] ,F ,intnat , ,ls-int-ls-nat ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≥ j ↔ ¬ i < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (# vals0, i + n→i(# vals), n0)]]