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Proof step 18 from proof okarray-put-02 (previous step)

okarray(refval(r0), byte_type, st[r0 -- _length] .intval, st) ⊦ r0 = jvmref, ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j, okreftype(refval(r0), mkarraytype(byte_type), st[r0 -- j ', byteval(by)]) ∧ r0 -- _length ∈ st ∧ st[r0 -- _length] = intval(st[r0 -- _length] .intval) ∧ ¬ st[r0 -- _length] .intval < 0 ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r0 -- j ', byteval(by)]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_bytevalue((j0 = j ⊃ byteval(by); st[r0 -- j0 '])))

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)
Proof step 17:
okarray(refval(r0), byte_type, st[r0 -- _length] .intval, st) ⊦ r0 = jvmref, ¬ j < 0 ∧ ¬ st[r0 -- _length] .intval ≤ j, is_referencevalue(refval(r0)) ∧ ( refval(r0) .refval ≠ jvmref → refval(r0) .refval -- _type ∈ st[r0 -- j ', byteval(by)] ∧ is_typevalue(st[r0 -- j ', byteval(by)][refval(r0) .refval -- _type]) ∧ (st[r0 -- j ', byteval(by)][refval(r0) .refval -- _type]) .type ≤ mkarraytype(byte_type)) ∧ r0 -- _length ∈ st ∧ st[r0 -- _length] = intval(st[r0 -- _length] .intval) ∧ ¬ st[r0 -- _length] .intval < 0 ∧ is_arrayref(r0, st[r0 -- _length] .intval, st[r0 -- j ', byteval(by)]) ∧ (0 ≤ j0 ∧ j0 < st[r0 -- _length] .intval → is_bytevalue((j0 = j ⊃ byteval(by); st[r0 -- j0 '])))

Rule argument

[crewrite-arg: okreftype , F , [st, ty, val] → [st[r0 -- j ', byteval(by)], mkarraytype(byte_type), refval(r0)] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- j ', byteval(by)], mkarraytype(byte_type), refval(r0))]]