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Proof step 3 from proof exactref-put-01 (previous step)

r ∈ st, r ≠ jvmref → r -- _type ∈ st ∧ is_typevalue(st[r -- _type]) ∧ st[r -- _type] .type = ty ⊦ r0 = r, exactreftype(refval(r), ty, st[r0 -- sk, val])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ exactreftype(val, ty, st) ↔ is_referencevalue(val) ∧ val .refval ∈ st ∧ (val .refval ≠ jvmref → val .refval -- _type ∈ st ∧ is_typevalue(st[val .refval -- _type]) ∧ st[val .refval -- _type] .type = ty)

Rule argument

[crewrite-arg: exactreftype , F , [st, ty, val] → [st[r0 -- sk, val], ty, refval(r)] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_referencevalue(refval(r))], [CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ r ∈ st[r0 -- sk, val] ↔ r = r0 ∨ r ∈ st], [CSIMPSEQ : ⊦ r ≠ r0 → ( r -- sk ∈ st[r0 -- sk0, val] ↔ r -- sk ∈ st)], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRATERMS : (st[r0 -- sk, val], ty, refval(r))]]