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Proof step 15 from proof isarray-putbar (previous step)

st[r1 -- _length] = intval(i0), st[r1 -- _type] = typeval(mkarraytype(byte_type)), r1 ∈ st, r1 -- _type ∈ st, is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), is_arrayref(r1, i0, st), r1 -- _length ∈ st, 0 ≤ i0, ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r1 -- j ']), ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st) ⊦ r1 = jvmref, okreftype(refval(r1), mkarraytype(byte_type), st) ∧ r1 ≠ jvmref ∧ r1 -- _length ∈ st ∧ is_integervalue(st[r1 -- _length]) ∧ 0 ≤ st[r1 -- _length] .intval ∧ is_arrayref(r1, st[r1 -- _length] .intval, st) ∧ (∀ j. 0 ≤ j ∧ j < st[r1 -- _length] .intval → oktype(st[r1 -- j '], byte_type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 14:
st[r1 -- _type] = typeval(mkarraytype(byte_type)), st[r1 -- _length] = intval(i0), 0 ≤ i0, r1 -- _length ∈ st, is_arrayref(r1, i0, st), is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), r1 -- _type ∈ st, r1 ∈ st, ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r1 -- j ']) ⊦ r1 = jvmref, okreftype(refval(r1), mkarraytype(byte_type), st) ∧ (0 ≤ j ∧ j < i0 → is_bytevalue(st[r1 -- j ']))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ intval(i) .intval = i], [CSIMPSEQ : ⊦ is_integervalue(intval(i))], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i])]]