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Proof step 20 from proof getarray-offset (previous step)

j ≤ 1 + j0, 0 ≤ j, 0 ≤ j0, 0 < j, 1 < j, j0 ≤ j, 0 < j0, ∀ 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 - 1, st) + st[r -- (i + j - 1) '] ' = 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 15:
⊦ j ≤ 0 → getarray(r, i, j, st) = []
Proof step 16:
⊦ getarray(r, i, 1, st) = st[r -- i '] '
Proof step 19:
j - j0 ≤ 0, j ≤ 1 + j0, 0 ≤ j, 0 ≤ j0, 0 < j, 1 < j, j0 ≤ j, 0 < j0, ∀ 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 - 1, st) + st[r -- (i + j - 1) '] ' = getarray(r, i, j0, st) + []

Rule argument

[crewrite-arg: getArray-zero , F , [st, j, i, r] → [st, j - j0, i + j0, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1)], [CSIMPSEQ : ⊦ i0 < i + j0 ∧ ¬ j < j0 → i0 ≠ i + j], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPSEQ : ⊦ i + j - i = j], [CSIMPSEQ : ⊦ vals + vals0 = vals + vals1 ↔ vals0 = vals1], [CSIMPSEQ : ⊦ (vals + vals0) + vals1 = vals + vals0 + vals1])], [EXTRATERMS : (st, j - j0, i + j0, r)]]