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Proof step 13 from proof getba-eq (previous step)

0 ≤ i1, 0 ≤ i, ∀ i0. ¬ i0 < i1 ∧ ¬ i1 + i ≤ i0 → st[r -- i0 '] = st[r1 -- i0 '], ∀ r1, r, st, i1, i0. i→n(i0) < i→n(i) → ( 0 ≤ i0 ∧ 0 ≤ i1 ∧ (∀ i2. ¬ i2 < i1 ∧ ¬ i1 + i0 ≤ i2 → st[r -- i2 '] = st[r1 -- i2 ']) → getbytearray(r, i1, i0, st) = getbytearray(r1, i1, i0, st)) ⊦ getbytearray(r, i1, i, st) = getbytearray(r1, i1, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 < j → getbytearray(r, i, j, st) = st[r -- i '] .byteval + getbytearray(r, i + 1, j - 1, st)
Proof step 2:
⊦ getbytearray(r, i, 0, st) = []
Proof step 12:
0 < i, 0 ≤ i1, 0 ≤ i, ∀ i0. ¬ i0 < i1 ∧ ¬ i1 + i ≤ i0 → st[r -- i0 '] = st[r1 -- i0 '], ∀ r1, r, st, i1, i0. i→n(i0) < i→n(i) → ( 0 ≤ i0 ∧ 0 ≤ i1 ∧ (∀ i2. ¬ i2 < i1 ∧ ¬ i1 + i0 ≤ i2 → st[r -- i2 '] = st[r1 -- i2 ']) → getbytearray(r, i1, i0, st) = getbytearray(r1, i1, i0, st)) ⊦ st[r -- i1 '] .byteval + getbytearray(r, i1 + 1, i - 1, st) = getbytearray(r1, i1, i, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)])], [EXTRATERMS : (st, i, i1, r)]]