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Proof step 21 from proof copy-bet-bet (previous step)

j0 = 2 * i0 + j - i + 1, 2 * i0 + j = (i + j0) + 1, i0 + j = i + 1, i0 ≤ i, 0 < j, i0 ≤ j0, j0 < i, i0 < i, ∀ j1, i0, i, j0, r, st. i→n(j1) < i→n(j) → ( true → ( i0 < i ∧ i < i0 + j1 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r, i0, j1, st)[r -- j0 ']) = st[r -- (i + j1 - (i0 + j1 - j0 + 1) % (i - i0) + 1) '])) ⊦ st[r -- (i + j - 1) '] = st[r -- (i + j - 1 + (i - j0) % (i - i0)) '], i = j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
i0 + j = i + 1, 2 * i0 + j ≤ 2 * i, 0 < j, i0 ≤ i, i0 < i, ∀ j1, i0, i, j0, r, st. i→n(j1) < i→n(j) → ( true → ( i0 < i ∧ i < i0 + j1 ∧ i0 ≤ j0 ∧ j0 < i0 + j1 → (arraycopy(r, i, r, i0, j1, st)[r -- j0 ']) = st[r -- (i + j1 - (i0 + j1 - j0 + 1) % (i - i0) + 1) '])) ⊦ 2 * i0 + j = 2 * i + 1, st[r -- (i + j - 1) '] = st[r -- (i + j - 1 + (2 * i + 1 - 2 * i0 + j) % (i - i0)) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i - j < i0 ↔ i < j + i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ 1 * i = i], [CSIMPSEQ : ⊦ i + j ≤ ((* i1)) * i + j0 ↔ j ≤ (i1 - 1) * i + j0], [CSIMPSEQ : ⊦ i ≤ j - i0 ↔ i + i0 ≤ j], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i + i = 2 * i], [CSIMPSEQ : ⊦ i - (j - j0) = i + j0 - j], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ i * j = j * i])]]