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Proof step 11 from proof getarray-addarray-03 (previous step)

0 ≤ i1, 0 < i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1, addarray(r, val, i1, st)[r -- i1 ', val]) = mklist(val, i→n(i1))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i0 < i ∨ i + j ≤ i0 → getarray(r, i, j, st[r0 -- i0 ', val]) = getarray(r, i, j, st)
Proof step 10:
i1 < 0 ∨ 0 + i1 ≤ i1, 0 ≤ i1, 0 < i1, ∀ st, val, r, i0. i→n(i0) < i→n(i1 + 1) → (0 ≤ i0 → getarray(r, 0, i0, addarray(r, val, i0, st)) = mklist(val, i→n(i0))) ⊦ getarray(r, 0, i1, addarray(r, val, i1, st)) = mklist(val, i→n(i1))

Rule argument

[speclemmaarg: , i0 < i ∨ i + j ≤ i0 → getarray(r, i, j, st[r0 -- i0 ', val]) = getarray(r, i, j, st) ,[val, i0, r0, st, j, i, r] → [val, i1, r, addarray(r, val, i1, st), i1, 0, r] ,F ,storearrays , ,getarray-put-05 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < i])], [EXTRATERMS : (val, i1, r, addarray(r, val, i1, st), i1, 0, r)]]