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Proof step 175 from proof putarray-addarray-override (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 173:
⊦ n→i(# vals) ≤ i → (addarray(r, ty, vals, st)[r -- i ']) = st[r -- i ']
Proof step 174:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]

Rule argument

[crewrite-arg: add-at-gr , F , [i, st, vals, ty, r] → [i0, st, vals0, ty, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i→n(i) ≤ n → ¬ n→i(n) < i])], [EXTRATERMS : (i0, st, vals0, ty, r0)]]