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Proof step 10 from proof putar-getar-01 (previous step)

0 ≤ i0, ∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, st[r -- i '] ' + getarray(r, i + 1, i0, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = getarray(r, i, i0 + 1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j → getarray(r, i, j, st) = st[r -- i '] ' + getarray(r, i + 1, j - 1, st)
Proof step 9:
0 < i0 + 1, 0 ≤ i0, ∀ r, r0, i, j, st. r = r0 ∨ getarray(r, i, j, putArray(vals0, r0, i, st)) = getarray(r, i, j, st) ⊦ r = r0, st[r -- i '] ' + getarray(r, i + 1, i0, putArray(vals0, r0, i + 1, st)[r0 -- i ', val]) = st[r -- i '] ' + getarray(r, i + 1, i0 + 1 - 1, st)

Rule argument

[crewrite-arg: get-rec-01, F, [st, j, i, r] → [st, i0 + 1, i, r]]

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 : (st, i0 + 1, i, r)]]