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Proof step 13 from proof getbar-add-01 (previous step)

∀ st, vals, ty, i, r0, r, j0. i→n(j0) < i→n(j) → (true → r = r0 ∨ getbytearray(r, i, j0, addarray(r0, ty, vals, st)) = getbytearray(r, i, j0, st)) ⊦ getbytearray(r, i, j, addarray(r0, ty, vals, st)) = getbytearray(r, i, j, st), r = r0

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 4:
¬ 0 < j, ∀ st, vals, ty, i, r0, r, j0. i→n(j0) < i→n(j) → (true → r = r0 ∨ getbytearray(r, i, j0, addarray(r0, ty, vals, st)) = getbytearray(r, i, j0, st)) ⊦ getbytearray(r, i, j, addarray(r0, ty, vals, st)) = getbytearray(r, i, j, st), r = r0
Proof step 12:
0 < j, ∀ st, vals, ty, i, r0, r, j0. i→n(j0) < i→n(j) → (true → r = r0 ∨ getbytearray(r, i, j0, addarray(r0, ty, vals, st)) = getbytearray(r, i, j0, st)) ⊦ (addarray(r0, ty, vals, st)[r -- i ']) .byteval + getbytearray(r, i + 1, j - 1, addarray(r0, ty, vals, st)) = getbytearray(r, i, j, st), r = r0

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] → [addarray(r0, ty, vals, st), j, i, r] ,F ,storearrays , ,getbar-rec ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r0, ty, vals, st), j, i, r)]]