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Proof step 9 from proof getarray-addarray-05 (previous step)

0 ≤ i, i ≤ i0, 0 ≤ i0, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (i ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, 0, i, addarray(r, val, j0, st)) = mklist(val, i→n(i))) ⊦ getarray(r, 0, i, addarray(r, val, i0, st)[r -- i0 ', val]) = mklist(val, i→n(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i0 < i ∨ i + j ≤ i0 → getarray(r, i, j, st[r -- i0 ', val]) = getarray(r, i, j, st)
Proof step 8:
i0 < 0 ∨ 0 + i ≤ i0, 0 ≤ i, i ≤ i0, 0 ≤ i0, ∀ st, val, r, i, j0. i→n(j0) < i→n(i0 + 1) → (i ≤ j0 ∧ 0 ≤ i ∧ 0 ≤ j0 → getarray(r, 0, i, addarray(r, val, j0, st)) = mklist(val, i→n(i))) ⊦ getarray(r, 0, i, addarray(r, val, i0, st)) = mklist(val, i→n(i))

Rule argument

[speclemmaarg: , i0 < i ∨ i + j ≤ i0 → getarray(r, i, j, st[r -- i0 ', val]) = getarray(r, i, j, st) ,[val, i0, st, j, i, r] → [val, i0, addarray(r, val, i0, st), i, 0, r] ,F ,storearrays , ,getarray-put-01 ]

Additional information

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