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Proof step 9 from proof getbar-add-01 (previous step)

0 ≤ i0, ∀ st, vals, ty, i, r0, r, j0. i→n(j0) < i→n(i0 + 1) → (true → r = r0 ∨ getbytearray(r, i, j0, addarray(r0, ty, vals, st)) = getbytearray(r, i, j0, st)) ⊦ r = r0, st[r -- i '] .byteval ' + getbytearray(r, i + 1, i0, addarray(r0, ty, vals, st)) = getbytearray(r, i, i0 + 1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j → getbytearray(r, i, j, st) = st[r -- i '] .byteval + getbytearray(r, i + 1, j - 1, st)
Proof step 8:
0 < i0 + 1, 0 ≤ i0, ∀ st, vals, ty, i, r0, r, j0. i→n(j0) < i→n(i0 + 1) → (true → r = r0 ∨ getbytearray(r, i, j0, addarray(r0, ty, vals, st)) = getbytearray(r, i, j0, st)) ⊦ r = r0, st[r -- i '] .byteval ' + getbytearray(r, i + 1, i0, addarray(r0, ty, vals, st)) = st[r -- i '] .byteval + getbytearray(r, i + 1, i0 + 1 - 1, st)

Rule argument

[speclemmaarg: , 0 < j → getbytearray(r, i, j, st) = st[r -- i '] .byteval + getbytearray(r, i + 1, j - 1, st) ,[st, j, i, r] → [st, i0 + 1, i, r] ,F ,storearrays , ,getbar-rec ]

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 ↔ false)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, i0 + 1, i, r)]]