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Proof step 17 from proof bar-neq-soffset (previous step)

getbytearray(r, i0, j0, st) = getbytearray(r0, i0, j0, st0), i + j ≤ i0 + j0, i0 ≤ i ⊦ getbytearray(r, i, j, st) = getbytearray(r0, i, j, st0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 ≤ j0 ∧ j0 ≤ j → getbytearray(r, i, j, st) = getbytearray(r, i, j0, st) + getbytearray(r, i + j0, j - j0, st)
Proof step 2:
⊦ j < 0 → getbytearray(r, i, j, st) = []
Proof step 16:
0 ≤ i - i0 ∧ i - i0 ≤ j0, getbytearray(r, i0, i - i0, st) + getbytearray(r, i0 + (i - i0), j0 - (i - i0), st) = getbytearray(r0, i0, j0, st0), i + j ≤ i0 + j0, i0 ≤ i ⊦ getbytearray(r, i, j, st) = getbytearray(r0, i, j, st0)

Rule argument

[crewrite-arg: getbar-anyrec , F , [j0, j, r, i, st] → [i - i0, j0, r, i0, st] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i + j < j ↔ i < 0])], [EXTRATERMS : (i - i0, j0, r, i0, st)]]