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Proof step 33 from proof copy-bet-bet (previous step)

i0 + (j - 1) ≤ i ∧ i0 ≤ j0 ∧ j0 < i0 + (j - 1), j0 < i0 + j, i0 ≤ j0, i < i0 + j, i0 < i, 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) '])) ⊦ (st[r -- (i0 + j - 1) ', st[r -- (i + j - 1) ']][r -- ((j0 - i0) + i) ']) = st[r -- (i + j - (i0 + j - j0 + 1) % (i - i0) + 1) '], i0 + j = j0 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
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) '])) ⊦ ((2 * i0 + j = (i + j0) + 1 ⊃ st[r -- (i + j - 1) ']; st[r -- (i + j0 - i0) '])) = st[r -- (i + j - 1 + (i - j0) % (i - i0)) '], i = j0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i + j < i + i0 ↔ j < i0], [CSIMPSEQ : ⊦ i < j + 1 ↔ i ≤ j], [CSIMPSEQ : ⊦ i + j = i + i0 ↔ j = i0], [CSIMPSEQ : ⊦ i + j - i0 + j = i - i0], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPSEQ : ⊦ i < j - i0 ↔ i + i0 < j], [CSIMPSEQ : ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1)], [CSIMPSEQ : ⊦ i - j ≤ i0 ↔ i ≤ j + i0], [CSIMPSEQ : ⊦ i + i = 2 * i], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + (j - i0) = i + j - i0])]]