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Proof step 12 from proof getarray-put-01 (previous step)

i0 < i ∨ i + j ≤ i0, ∀ j0, i0, i, r, st, val. i→n(j0) < i→n(j) → (i0 < i ∨ i + j0 ≤ i0 → getarray(r, i, j0, st[r -- i0 ', val]) = getarray(r, i, j0, st)) ⊦ getarray(r, i, j, st[r -- i0 ', val]) = getarray(r, i, j, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 2:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 11:
0 < j, i0 < i ∨ i + j ≤ i0, ∀ j0, i0, i, r, st, val. i→n(j0) < i→n(j) → (i0 < i ∨ i + j0 ≤ i0 → getarray(r, i, j0, st[r -- i0 ', val]) = getarray(r, i, j0, st)) ⊦ (st[r -- i0 ', val][r -- i ']) ' + getarray(r, i + 1, j - 1, st[r -- i0 ', val]) = getarray(r, i, j, st)

Rule argument

[crewrite-arg: get-rec-01 , F , [st, j, i, r] → [st[r -- i0 ', val], j, i, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])], [EXTRATERMS : (st[r -- i0 ', val], j, i, r)]]