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Proof step 16 from proof at=get (previous step)

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

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 15:
1 < j, true, ∀ r, st, i, j0. i→n(j0) < i→n(j) → (true → (0 ≤ i ∧ i < j0 → st[r -- i '] = (getarray(r, 0, j0, st)[i→n(i)]))) ⊦ 0 ≤ i ∧ i < j → st[r -- i '] = (getarray(r, 0, j - 1, st) + st[r -- (0 + j - 1) '])[i→n(i)]

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, j, 0, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ 0 ≤ i → (i < 1 ↔ i = 0)], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPSEQ : ⊦ (val ')[0] = val])], [EXTRATERMS : (st, j, 0, r)]]