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Proof step 8 from proof validref-putbar (previous step)

st[r0 -- _length] = intval(i0), 0 ≤ i0, r0 ∈ st, is_arrayref(r0, i0, st), r0 -- _length ∈ st, okreftype(refval(r0), mkarraytype(byte_type), st), validref(str, r, ty, st), ∀ j. ¬ j < 0 ∧ ¬ i0 ≤ j → is_bytevalue(st[r0 -- j ']), ∀ str, r, ty, st, r0, i. validref(str, r, ty, st) ∧ okbytearray(r0, st) → r = r0 ∨ validref(str, r, ty, putByteArray(bytes0, r0, i, st)) ⊦ r0 = jvmref, st[r0 -- _type] .type .type = byte_type, r = r0, validref(str, r, ty, putByteArray(bytes0, r0, i + 1, st)[r0 -- i ', byteval(by)])

User applied rule insert rewrite lemma

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)

Rule argument

[speclemmaarg: , 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) ,[st, ty, val] → [st, mkarraytype(byte_type), refval(r0)] ,F ,okfuns , ,okreftype ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ ty ≤ mkarraytype(byte_type) ↔ ty = mkarraytype(byte_type)], [CSIMPSEQ : ⊦ mkarraytype(ty) .type = ty])], [EXTRATERMS : (st, mkarraytype(byte_type), refval(r0))]]