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Proof step 93 from proof putarray-addarray-override (previous step)

0 ≤ i0, 0 ≤ i, i + n→i(# vals) ≤ n→i(# vals0), i0 < i ∨ n→i(# vals) + i ≤ i0, i0 < 0 ∨ i + n→i(# vals) + n→i(# restn(i→n(i) + # vals, vals0)) ≤ i0 ⊦ (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, ¬ i0 < 0 ∧ ¬ # vals0 ≤ i→n(i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 77:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]
Proof step 92:
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 ⊦ (addarray(r0, ty, vals0, st)[r0 -- i0 ']) = st[r0 -- i0 ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ n→i(n) < 0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]