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Proof step 8 from proof copy-lower (previous step)

(arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = (st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']][r0 -- j0 ']), j0 < i0, 0 < j, ∀ j1, j0, i0, r, i, r0, st. i→n(j1) < i→n(j) → (j0 < i0 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r0 -- j0 ']) ⊦ (arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = st[r0 -- j0 ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(arraycopy(r, i, r0, i0, j - 1, st[r0 -- (i0 + j - 1) ', st[r -- (i + j - 1) ']])[r0 -- j0 ']) = ((i0 + j = j0 + 1 ⊃ st[r -- (i + j - 1) ']; st[r0 -- j0 '])), j0 < i0, 0 < j, ∀ j1, j0, i0, r, i, r0, st. i→n(j1) < i→n(j) → (j0 < i0 → (arraycopy(r, i, r0, i0, j1, st)[r0 -- j0 ']) = st[r0 -- j0 ']) ⊦ ((i0 + j = j0 + 1 ⊃ st[r -- (i + j - 1) ']; st[r0 -- j0 '])) = st[r0 -- j0 ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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]))])]]