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Proof step 2 from proof init-at (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ j ≤ i ∧ i < j + n→i(# vals) → (addarray(r, vals, j, st)[r -- i ']) = vals[i→n(i - j)]

Rule argument

[crewrite-arg: init-at-01 , F , [i, st, j, vals, r] → [i, st, 0, vals, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i - 0 = i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)])], [EXTRATERMS : (i, st, 0, vals, r)]]