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Proof step 9 from proof addobj-union (previous step)

newref(r, st), newref(r, st0) ⊦ (addobj(r, class, fis, st) ∪ st0)[r -- sk] = (addobj(r, class, fis, st ∪ st0)[r -- sk]), r = jvmref, ¬ sk ∈ fis ∧ sk ≠ _type

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 6:
⊦ sk ∈ fis → (addobj(r, class, fis, st)[r -- sk]) = fis[sk]
Proof step 7:
⊦ sk ∈ fis → (addobj(r, class, fis, st)[r -- sk]) = fis[sk]
Proof step 8:
¬ _type ∈ fis ⊦ (addobj(r, class1, fis, st)[r -- _type]) = typeval(mkclasstype(class1))

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r -- sk, st0, addobj(r, class, fis, st)] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ typeval(ty) = typeval(ty0) ↔ ty = ty0], [CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (r -- sk, st0, addobj(r, class, fis, st))]]