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

getarray(r, i, 2 + i2, st) = val ' + vals, (~1) ≤ i2, 0 < i2, val ∈ getarray(r, i, 2 + i2, st), ∀ i1, r, i, st. i→n(i1) < i→n(i2 + 1) → (0 ≤ i1 → getarray(r, i, i1 + 1, st) .rest = getarray(r, i + 1, i1, st)) ⊦ vals = getarray(r, i + 1, i2, st) + st[r -- (i + i2 + 1) '] '

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 1 < j → getarray(r, i, j, st) = getarray(r, i, j - 1, st) + st[r -- (i + j - 1) ']
Proof step 23:
1 < 2 + i2, getarray(r, i, 2 + i2 - 1, st) + st[r -- (i + 2 + i2 - 1) '] = val ' + vals, (~1) ≤ i2, 0 < i2, val ∈ getarray(r, i, 2 + i2 - 1, st) + st[r -- (i + 2 + i2 - 1) '], ∀ i1, r, i, st. i→n(i1) < i→n(i2 + 1) → (0 ≤ i1 → getarray(r, i, i1 + 1, st) .rest = getarray(r, i + 1, i1, st)) ⊦ vals = getarray(r, i + 1, i2, st) + st[r -- (i + i2 + 1) '] '

Rule argument

[crewrite-arg: getArray-rec, F, [st, j, i, r] → [st, 2 + i2, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, 2 + i2, i, r)]]