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Proof step 10 from proof okarray-02 (previous step)

⊦ r = r0, okreftype(refval(r), mkarraytype(byte_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_bytevalue(st[r -- j '])) ↔ okreftype(refval(r), mkarraytype(byte_type), st) ∧ r ≠ jvmref ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ 0 ≤ st[r -- _length] .intval ∧ is_arrayref(r, st[r -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r -- _length] .intval → oktype(st[r -- j '], byte_type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j < st[r -- _length] .intval, okreftype(refval(r), mkarraytype(byte_type), st), r -- _length ∈ st, is_integervalue(st[r -- _length]), is_arrayref(r, st[r -- _length] .intval, st), 0 ≤ j, 0 < st[r -- _length] .intval, r ∈ st, 0 ≤ st[r -- _length] .intval, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_bytevalue(st[r -- j ']) ⊦ r = r0, r = jvmref, is_bytevalue(st[r -- j '])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)])]]