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Proof step 12 from proof del-addobj (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 4:
⊦ ¬ r ∈ st -- r ∧ (∀ r0, sk. r ≠ r0 → (r0 -- sk ∈ st ↔ r0 -- sk ∈ st -- r) ∧ st[r0 -- sk] = (st -- r)[r0 -- sk])
Proof step 11:
¬ r0 ∈ addobj(r0, class, fis, st) -- r0 ∧ (∀ r1, sk. r0 ≠ r1 → (r1 -- sk ∈ addobj(r0, class, fis, st) ↔ r1 -- sk ∈ addobj(r0, class, fis, st) -- r0) ∧ (addobj(r0, class, fis, st)[r1 -- sk]) = (addobj(r0, class, fis, st) -- r0)[r1 -- sk]), newref(r0, st) ⊦ (addobj(r0, class, fis, st) -- r0)[r0 -- sk] = st[r0 -- sk], r0 = jvmref

Rule argument

[speclemmaarg: , ¬ r ∈ st -- r ∧ (∀ r0, sk. r ≠ r0 → (r0 -- sk ∈ st ↔ r0 -- sk ∈ st -- r) ∧ st[r0 -- sk] = (st -- r)[r0 -- sk]) ,[r, st] → [r0, addobj(r0, class, fis, st)] ,F ,storefuns , ,deleteref ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r0, addobj(r0, class, fis, st))]]