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Proof step 9 from proof is_array-byte-noref (previous step)

st[r -- i '] = refval(r1), st[r -- _type] = typeval(mkarraytype(byte_type)), 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)), i < st[r -- _length] .intval, r ∈ st, 0 ≤ i, 0 < st[r -- _length] .intval, r -- _type ∈ st ⊦ r = jvmref

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 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 5:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 8:
st[r -- _type] = typeval(mkarraytype(byte_type)), st[r -- i '] = refval(r1), 0 ≤ st[r -- _length] .intval, r -- _type ∈ st, 0 < st[r -- _length] .intval, 0 ≤ i, r ∈ st, i < st[r -- _length] .intval, is_arrayref(r, st[r -- _length] .intval, st), is_integervalue(st[r -- _length]), r -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r -- _length] .intval ≤ j → is_bytevalue(st[r -- j ']) ⊦ r = jvmref

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_typevalue(typeval(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) = mkarraytype(ty0) ↔ ty = ty0], [CSIMPSEQ : ⊦ typeval(ty) .type = ty], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [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))])]]