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Proof step 3 from proof succ-1init (previous step)

i0 < n→i(# vals), 0 ≤ i0 ⊦ vals = [], (addarray(r, ty, val ' + vals, st)[r -- (i0 + 1) ']) = vals[i→n(i0)]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 ≤ i ∧ i < n→i(# vals) → (addarray(r, ty, vals, st)[r -- i ']) = vals[i→n(i)]

Rule argument

[crewrite-arg: add-at-ok , F , [i, st, vals, ty, r] → [i0 + 1, st, val ' + vals, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (val ' + vals)[n + 1] = vals[n]], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ # (vals + vals0) = # vals + # vals0], [CSIMPSEQ : ⊦ # val ' = 0 +1], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i0 + 1, st, val ' + vals, ty, r)]]