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Proof step 21 from proof isarray-putbar (previous step)

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)), is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), r1 ∈ st, ∀ r1, i, st. is_array(r1, putByteArray(bytes0, r1, i, st)) ∧ okbytearray(r1, st) → is_array(r1, st) ⊦ r1 = jvmref, okarray(r1, st[r1 -- _type] .type .type, st) ∧ is_arraytype(st[r1 -- _type] .type) ∧ is_typevalue(st[r1 -- _type]) ∧ r1 -- _type ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ 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 8:
⊦ oktype(val, byte_type, st) ↔ is_bytevalue(val)
Proof step 20:
st[r1 -- _type] .type = mkarraytype(byte_type), r1 ∈ st, 0 ≤ st[r1 -- _length] .intval, is_typevalue(st[r1 -- _type]), r1 -- _type ∈ st, is_array(r1, putByteArray(bytes0, r1, i + 1, st)[r1 -- i ', byteval(by)]), is_arrayref(r1, st[r1 -- _length] .intval, st), is_integervalue(st[r1 -- _length]), r1 -- _length ∈ st, ∀ j. ¬ j < 0 ∧ ¬ st[r1 -- _length] .intval ≤ 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, okarray(r1, byte_type, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_arraytype(mkarraytype(ty))], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty], [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))])]]