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Proof step 12 from proof getarray-offset (previous step)

0 ≤ j, 0 ≤ j0, j0 ≤ 1, j ≤ 1, j0 ≤ j, ∀ j1, j0, r, i, st. i→n(j1) < i→n(j) → (j0 ≤ j1 ∧ 0 ≤ j0 → getarray(r, i, j1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j1 - j0, st)) ⊦ getarray(r, i, j, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j - j0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 9:
¬ j ≤ 0, 0 ≤ j, 0 ≤ j0, j0 ≤ 1, j ≤ 1, j0 ≤ j, ∀ j1, j0, r, i, st. i→n(j1) < i→n(j) → (j0 ≤ j1 ∧ 0 ≤ j0 → getarray(r, i, j1, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j1 - j0, st)) ⊦ getarray(r, i, j, st) = getarray(r, i, j0, st) + getarray(r, i + j0, j - j0, st)
Proof step 10:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 11:
⊦ getarray(r, i, j, st) = [] ↔ j ≤ 0

Rule argument

[crewrite-arg: getArray-zero, F, [st, j, i, r] → [st, j, i, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ 0 - i = ~ i], [CSIMPSEQ : ⊦ [] + vals = vals], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1], [CSIMPSEQ : ⊦ ~ i ≤ j ↔ 0 ≤ i + j], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i])], [EXTRATERMS : (st, j, i, r)]]