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Proof step 18 from proof copy-bet-bet (previous step)

2 * i0 + j ≤ 2 * (i0 + j - 1), 1 < j, 0 < j, ∀ 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 * (i0 + j - 1) + 1, st[r -- (2 * j + i0 - 2) '] = st[r -- (2 * j + i0 - 2 + (2 * (i0 + j - 1) + 1 - 2 * i0 + j) % (j - 1)) ']

User applied rule cut formula

And obtained the following new goals

Proof step 17:
2 * (i0 + j - 1) + 1 - 2 * i0 + j = j - 1, 2 * i0 + j ≤ 2 * (i0 + j - 1), 1 < j, 0 < j, ∀ 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 * (i0 + j - 1) + 1, st[r -- (2 * j + i0 - 2) '] = st[r -- (2 * j + i0 - 2 + (2 * (i0 + j - 1) + 1 - 2 * i0 + j) % (j - 1)) ']

Rule argument

[fma-arg: 2 * (i0 + j - 1) + 1 - 2 * i0 + j = j - 1]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0], [CSIMPSEQ : ⊦ i + i = 2 * i], [CSIMPSEQ : ⊦ i * j + i * j0 = i * (j + j0)], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i * j + i = i * (j + 1)], [CSIMPSEQ : ⊦ i + (j - i) = j], [CSIMPSEQ : ⊦ 0 < i → (i * j = i * j0 ↔ j = j0)])], [EXTRAFMAS : (2 * (i0 + j - 1) + 1 - 2 * i0 + j = j - 1)]]