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Proof step 7 from proof stsubset-addobj (previous step)

st[r0 -- sk] = (addobj(r, class1, fis, st0)[r0 -- sk]), newref(r, st), r0 -- sk ∈ st, r0 -- sk ∈ addobj(r, class1, fis, st0), r0 ∈ st, r0 ∈ addobj(r, class1, fis, st0), ∀ rk. rk ∈ st → rk ∈ addobj(r, class1, fis, st0) ∧ st[rk] = (addobj(r, class1, fis, st0)[rk]) ⊦ r = jvmref, r0 -- sk ∈ st0 ∧ (addobj(r, class1, fis, st0)[r0 -- sk]) = st0[r0 -- sk]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ r0 → (addobj(r, class1, fis, st)[r0 -- sk]) = st[r0 -- sk]
Proof step 6:
r ≠ r0, st[r0 -- sk] = st0[r0 -- sk], newref(r, st), r0 -- sk ∈ st, r0 -- sk ∈ addobj(r, class1, fis, st0), r0 ∈ st, r0 ∈ addobj(r, class1, fis, st0), ∀ rk. rk ∈ st → rk ∈ addobj(r, class1, fis, st0) ∧ st[rk] = (addobj(r, class1, fis, st0)[rk]) ⊦ r = jvmref, r0 -- sk ∈ st0 ∧ st0[r0 -- sk] = st0[r0 -- sk]

Rule argument

[crewrite-arg: add-ref , F , [sk, r0, st, fis, class1, r] → [sk, r0, st0, fis, class1, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ st → ¬ newref(r, st)])], [EXTRATERMS : (sk, r0, st0, fis, class1, r)]]