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Proof step 6 from proof copy-in-lower (previous step)

j0 < i0 → ( r0 -- j0 ' ∈ 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) ']]), j0 < i0, 0 < j, ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ 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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i0 + j = j0 + 1, j0 < i0, 0 < j, r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- j0 ', st[r -- (i + j - 1) ']]), r0 ∈ arraycopy(r, i, r0, i0, j - 1, st[r0 -- j0 ', st[r -- (i + j - 1) ']]), ∀ j1, j0, i0, r0, r, i, st. i→n(j1) < i→n(j) → (true → (j0 < i0 → (r0 -- j0 ' ∈ arraycopy(r, i, r0, i0, j1, st) ↔ r0 -- j0 ' ∈ st))) ⊦ r0 -- j0 ' ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ ((* i)) + i0 - ((* j)) = (i - j) + i0], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ i - j = i0 ↔ i = i0 + j], [CSIMPSEQ : ⊦ i ' = i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i])]]