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Proof step 21 from proof okarray-copy-01 (previous step)

okarray(r0, byte_type, st), okarray(r, byte_type, st), 0 ≤ i, r0 ∈ st, r ∈ st, i + i1 < st[r0 -- _length] .intval, 0 ≤ i1, ∀ i0, i, r0, st, r, j0. i→n(j0) < i→n(i1 + 1) → ( okarray(r, byte_type, st) ∧ okarray(r0, byte_type, st) ∧ i + j0 ≤ st[r0 -- _length] .intval ∧ r ∈ st ∧ r0 ∈ st ∧ 0 ≤ i ∧ 0 ≤ j0 → r = jvmref ∨ r0 = jvmref ∨ okarray(r, byte_type, arraycopy(r0, i, r, i0, j0, st))) ⊦ r0 = jvmref, r = jvmref, okarray(r, byte_type, arraycopy(r0, i, r, i0, i1, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]))

User applied rule apply induction

And obtained the following new goals

Proof step 20:
okarray(r0, byte_type, st), okarray(r, byte_type, st), 0 ≤ i, r0 ∈ st, r ∈ st, i + i1 < st[r0 -- _length] .intval, 0 ≤ i1, ∀ i0, i, r0, st, r, j0. i→n(j0) < i→n(i1 + 1) → ( okarray(r, byte_type, st) ∧ okarray(r0, byte_type, st) ∧ i + j0 ≤ st[r0 -- _length] .intval ∧ r ∈ st ∧ r0 ∈ st ∧ 0 ≤ i ∧ 0 ≤ j0 → r = jvmref ∨ r0 = jvmref ∨ okarray(r, byte_type, arraycopy(r0, i, r, i0, j0, st))) ⊦ okarray(r, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ okarray(r0, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ i + i1 ≤ (st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']][r0 -- _length]) .intval ∧ r ∈ st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']] ∧ r0 ∈ st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']] ∧ 0 ≤ i ∧ 0 ≤ i1, r0 = jvmref, r = jvmref, okarray(r, byte_type, arraycopy(r0, i, r, i0, i1, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]))

Rule argument

[substlist-arg: [i0, i, r0, st, r, j0] → [i0, i, r0, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']], r, i1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j)], [CSIMPSEQ : ⊦ 0 ≤ i → abs(i) = i], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m])], [EXTRATERMS : (i0, i, r0, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']], r, i1)]]