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Proof step 25 from proof addobj-union-rew (previous step)

newref(r0, st), newref(r0, st0) ⊦ r0 = jvmref, (addobj(r0, class, fis, st ∪ st0)[r0 -- sk]) = (st ∪ addobj(r0, class, fis, st0))[r0 -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ sk ∈ fis ∧ sk ≠ _type → (addobj(r, class, fis, st)[r -- sk]) = st[r -- sk]
Proof step 18:
¬ (¬ sk ∈ fis ∧ sk ≠ _type), newref(r0, st), newref(r0, st0) ⊦ r0 = jvmref, (addobj(r0, class, fis, st ∪ st0)[r0 -- sk]) = (st ∪ addobj(r0, class, fis, st0))[r0 -- sk]
Proof step 24:
¬ sk ∈ fis ∧ sk ≠ _type, newref(r0, st), newref(r0, st0) ⊦ r0 = jvmref, (st ∪ st0)[r0 -- sk] = (st ∪ addobj(r0, class, fis, st0))[r0 -- sk]

Rule argument

[crewrite-arg: add-notin , F , [sk, st, fis, class, r] → [sk, st ∪ st0, fis, class, r0] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (sk, st ∪ st0, fis, class, r0)]]