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Proof step 17 from proof at=get-offset (previous step)

0 ≤ i1, 0 ≤ i1 + i0, i1 < j, 0 < j, 0 < j + i0, 0 ≤ i0, ∀ r, st, i1, i0, j0. i→n(j0) < i→n(j) → (0 ≤ i0 ∧ 0 < j0 + i0 ∧ 0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 + i0 ∧ 0 ≤ i1 → st[r -- (i1 + i0) '] = (getarray(r, i0, j0, st)[i→n(i1)])) ⊦ st[r -- (i1 + i0) '] = (getarray(r, i0, j, st)[i→n(i1)])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 2:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 16:
1 < j, 0 ≤ i1, 0 ≤ i1 + i0, i1 < j, 0 < j, 0 < j + i0, 0 ≤ i0, ∀ r, st, i1, i0, j0. i→n(j0) < i→n(j) → (0 ≤ i0 ∧ 0 < j0 + i0 ∧ 0 < j0 ∧ i1 < j0 ∧ 0 ≤ i1 + i0 ∧ 0 ≤ i1 → st[r -- (i1 + i0) '] = (getarray(r, i0, j0, st)[i→n(i1)])) ⊦ st[r -- (i1 + i0) '] = (getarray(r, i0, j - 1, st) + st[r -- (i0 + j - 1) '])[i→n(i1)]

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, j, i0, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ (val ')[0] = val])], [EXTRATERMS : (st, j, i0, r)]]