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Proof step 106 from proof putarray-addarray-override (previous step)

0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (putArray(vals, r0, i, addarray(r0, ty, vals0, st))[r0 -- i0 ']) = st[r0 -- i0 '], ¬ i0 < 0 ∧ ¬ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , i < j ∨ n→i(# vals) + j ≤ i → (putArray(vals, r, j, st)[r0 -- i ']) = st[r0 -- i '] ,[i, r0, st, j, r, vals] → [i0, r0, addarray(r0, ty, vals0, st), i, r0, vals] ,F ,storearrays , ,putar-atother ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j ∧ j < i + n→i(# vals) → (putArray(vals, r, i, st) [r -- j ' ] ) = vals[i→n(j - i)]], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i < i + j ↔ 0 < j], [CSIMPSEQ : 0 ≤ i ⊦ ((* i)) < n→i(n) ↔ i→n(i) < n], [CSIMPSEQ : ⊦ 0 < n ↔ n ≠ 0], [CSIMPSEQ : ⊦ # vals = 0 ↔ vals = []], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ ¬ n→i(n) < 0])], [EXTRATERMS : (i0, r0, addarray(r0, ty, vals0, st), i, r0, vals)]]