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Proof step 24 from proof getarray-in-01 (previous step)

0 < i1, i < i0 + i1, i0 ≤ i, ∀ r, st, i, i0, i2. i→n(i2) < i→n(i1) → (i0 ≤ i ∧ i < i0 + i2 ∧ 0 < i2 → st[r -- i '] ∈ getarray(r, i0, i2, st)) ⊦ st[r -- i '] ∈ getarray(r, i0, i1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 19:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 23:
1 < i1, 0 < i1, i < i0 + i1, i0 ≤ i, ∀ r, st, i, i0, i2. i→n(i2) < i→n(i1) → (i0 ≤ i ∧ i < i0 + i2 ∧ 0 < i2 → st[r -- i '] ∈ getarray(r, i0, i2, st)) ⊦ st[r -- i '] ∈ getarray(r, i0, i1 - 1, st) + st[r -- (i0 + i1 - 1) ']

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ 0 < i → (i ≤ 1 ↔ i = 1)], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ val ∈ val0 ' ↔ val = val0])], [EXTRATERMS : (st, i1, i0, r)]]