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Proof step 12 from proof okarray-copy-01 (previous step)

okreftype(refval(r0), mkarraytype(byte_type), st) ∧ r0 ≠ jvmref ∧ r0 -- _length ∈ st ∧ is_integervalue(st[r0 -- _length]) ∧ 0 ≤ st[r0 -- _length] .intval ∧ is_arrayref(r0, st[r0 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r0 -- _length] .intval → oktype(st[r0 -- j '], 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) ']])), is_bytevalue(st[r0 -- (i + i1) ']), okarray(r, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ okarray(r0, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ okreftype(val, ty, st) ↔ is_referencevalue(val) ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type ≤ ty)
Proof step 6:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 11:
st[r0 -- _type] .type = mkarraytype(byte_type), r0 -- _length ∈ st, is_integervalue(st[r0 -- _length]), is_arrayref(r0, st[r0 -- _length] .intval, st), okarray(r, byte_type, st), 0 ≤ i, r ∈ st, i + i1 < st[r0 -- _length] .intval, 0 ≤ i1, r0 -- _type ∈ st, is_typevalue(st[r0 -- _type]), 0 ≤ st[r0 -- _length] .intval, r0 ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j → is_bytevalue(st[r0 -- j ']), ∀ 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))) ⊦ r = jvmref, r0 = jvmref, okarray(r, byte_type, arraycopy(r0, i, r, i0, i1, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])), is_bytevalue(st[r0 -- (i + i1) ']), okarray(r, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']]) ∧ okarray(r0, byte_type, st[r -- (i0 + i1) ', st[r0 -- (i + i1) ']])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ is_referencevalue(refval(r))])]]