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Proof step 78 from proof cyclic-addobj (previous step)

fis .keys = instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), validfieldinits(fis, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ cyclic(str, r, addobj(r, class, fis, st)) ↔ (∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r)), r = jvmref

User applied rule case distinction

And obtained the following new goals

Proof step 60:
cyclic(str, r, addobj(r, class, fis, st)), fis .keys = instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), validfieldinits(fis, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ ∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r), r = jvmref
Proof step 77:
∃ fs. fs ' ∈ fis ∧ fs ' ∈ instfields(class) ∧ fis[fs '] = refval(r), fis .keys = instfields(class), newref(r, st), is_obj(str, r, addobj(r, class, fis, st)), validfieldinits(fis, st), ∀ fs, r0. fs ' × refval(r0) ∈ fis → ¬ junkref(str, r0, st) ∧ ¬ cyclic(str, r0, st) ⊦ cyclic(str, r, addobj(r, class, fis, st)), r = jvmref

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]