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Proof step 23 from proof addobj-union-rew (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]
Proof step 20:
⊦ ¬ sk ∈ fis ∧ sk ≠ _type → (addobj(r, class, fis, st)[r -- sk]) = st[r -- sk]
Proof step 21:
⊦ r -- sk ∈ addobj(r, class, fis, st) ↔ ¬ ¬ (sk ∈ fis ∨ sk = _type ∨ r -- sk ∈ st)
Proof step 22:
⊦ r -- sk ∈ addobj(r, class, fis, st) ↔ ¬ ¬ (sk ∈ fis ∨ sk = _type ∨ r -- sk ∈ st)

Rule argument

[speclemmaarg: ,¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk] ,[rk, st0, st] → [r0 -- sk, addobj(r0, class, fis, st0), st] ,F ,storefunsx , ,union-at-left ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ st0 → (st ∪ st0)[rk] = st0[rk]], [CSIMPSEQ : ⊦ ¬ rk ∈ st0 → (st ∪ st0)[rk] = st[rk]])], [EXTRATERMS : (r0 -- sk, addobj(r0, class, fis, st0), st)]]