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Proof step 21 from proof okarray-put-06 (previous step)

is_bytevalue(val), okarray(r, byte_type, st), r ∈ st ⊦ r = jvmref, okreftype(refval(r), mkarraytype(byte_type), st[r -- i ', val]) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- i ', val]) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → is_bytevalue(st[r -- i ', val][r -- j ']))

User applied rule insert rewrite lemma

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 20:
is_bytevalue(val), okarray(r, byte_type, st), r ∈ st ⊦ r = jvmref, is_referencevalue(refval(r)) ∧ ( refval(r) .refval ≠ jvmref → refval(r) .refval -- _type ∈ st[r -- i ', val] ∧ is_typevalue(st[r -- i ', val][refval(r) .refval -- _type]) ∧ (st[r -- i ', val][refval(r) .refval -- _type]) .type ≤ mkarraytype(byte_type)) ∧ r -- _length ∈ st ∧ is_integervalue(st[r -- _length]) ∧ is_arrayref(r, st[r -- _length] .intval, st[r -- i ', val]) ∧ (0 ≤ j ∧ j < st[r -- _length] .intval → is_bytevalue(st[r -- i ', val][r -- j ']))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st[r -- i ', val], mkarraytype(byte_type), refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- i ', val], mkarraytype(byte_type), refval(r))]]