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

¬ r0 -- sk ∈ addobj(r0, class, fis, st) -- r0, ¬ 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) ⊦ ∅[r0 -- sk] = st[r0 -- sk], r0 = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ¬ rk ∈ st → st[rk] = ∅[rk]
Proof step 7:
⊦ r ≠ r0 → (r -- sk ∈ addobj(r0, class1, fis, st) ↔ r -- sk ∈ st)
Proof step 8:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]

Rule argument

[speclemmaarg: ,¬ rk ∈ st → st[rk] = ∅[rk] ,[rk, st] → [r0 -- sk, st] ,F ,store ,javastore ,notmemlookup ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ∅[rk] = noval], [CSIMPSEQ : ⊦ r -- sk ∈ st -- r0 ↔ r ≠ r0 ∧ r -- sk ∈ st], [CSIMPSEQ : ⊦ r ≠ r0 → (st -- r)[r0 -- sk0] = st[r0 -- sk0]], [CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (r0 -- sk, st)]]