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Proof step 14 from proof putar-getar (previous step)

n→i(# vals0) = i1 + 1, getarray(r, i + 1, i1, putArray(vals0, r, i + 1, st)) + (putArray(vals0, r, i + 1, st)[r -- (1 + i + i1) ']) ' = vals0, 0 ≤ i1, 0 < i1, (putArray(vals0, r, i + 1, st)[r -- (1 + i + i1) ']) ∈ vals0 ⊦ vals0 = [], getarray(r, i + 1, i1, putArray(vals0, r, i + 1, st)) + vals0[i→n(i1)] ' = vals0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ j ≤ i ∧ i < n→i(# vals) + j → (putArray(vals, r, j, st)[r -- i ']) = vals[i→n(i - j)]

Rule argument

[crewrite-arg: putar-at , F , [i, st, j, r, vals] → [1 + i + i1, st, i + 1, r, vals0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ i + j - i + 1 = j - 1], [CSIMPSEQ : ⊦ i + j ≤ i0 + j ↔ i ≤ i0], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j ≤ i ↔ j ≤ 0])], [EXTRATERMS : (1 + i + i1, st, i + 1, r, vals0)]]