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Proof step 6 from proof addobj-getarray-01 (previous step)

0 ≤ i0, ∀ st, fis, class, i, r0, r, j0. i→n(j0) < i→n(i0 + 1) → (true → r = r0 ∨ getarray(r, i, j0, addobj(r0, class, fis, st)) = getarray(r, i, j0, st)) ⊦ getarray(r, i, i0 + 1, addobj(r0, class, fis, st)) = st[r -- i '] ' + getarray(r, i + 1, i0, st), r = r0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 5:
0 < i0 + 1, 0 ≤ i0, ∀ st, fis, class, i, r0, r, j0. i→n(j0) < i→n(i0 + 1) → (true → r = r0 ∨ getarray(r, i, j0, addobj(r0, class, fis, st)) = getarray(r, i, j0, st)) ⊦ (addobj(r0, class, fis, st)[r -- i ']) ' + getarray(r, i + 1, i0 + 1 - 1, addobj(r0, class, fis, st)) = st[r -- i '] ' + getarray(r, i + 1, i0, st), r = r0

Rule argument

[speclemmaarg: , 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st) ,[st, j, i, r] → [addobj(r0, class, fis, st), i0 + 1, i, r] ,F ,storearrays , ,get-rec-01 ]

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 : (addobj(r0, class, fis, st), i0 + 1, i, r)]]