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Proof step 24 from proof get-alleq (previous step)

0 < i1, ∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(i1 + 1) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, i1, st) + st[r -- (i + i1) '] ' = getarray(r0, i0, i1 + 1, st0) ↔ (∀ j. j ≤ i1 ∧ 0 ≤ j → st[r -- (i + j) '] = st0[r0 -- (i0 + j) '])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 23:
1 < i1 + 1, 0 < i1, ∀ j0, r, i, st, r0, i0, st0. i→n(j0) < i→n(i1 + 1) → (true → (getarray(r, i, j0, st) = getarray(r0, i0, j0, st0) ↔ (∀ j1. 0 ≤ j1 ∧ j1 < j0 → st[r -- (i + j1) '] = st0[r0 -- (i0 + j1) ']))) ⊦ getarray(r, i, i1, st) + st[r -- (i + i1) '] ' = getarray(r0, i0, i1 + 1 - 1, st0) + st0[r0 -- (i0 + i1 + 1 - 1) '] ↔ (∀ j. j ≤ i1 ∧ 0 ≤ j → st[r -- (i + j) '] = st0[r0 -- (i0 + j) '])

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st0, i1 + 1, i0, r0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st0, i1 + 1, i0, r0)]]