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Proof step 83 from proof maxpath-object (previous step)

validrefset(str, r, st) = ∅, st[r -- fs '] = refval(r0), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, st), cyclic(str, r, st), has_reffield((r ' + refs0) .last, st), dups(refs0), r ∈ refs0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 77:
⊦ refsset = refsset0 ↔ (∀ refs. refs ∈ refsset ↔ refs ∈ refsset0)
Proof step 82:
∀ refs. refs ∈ validrefset(str, r, st) ↔ refs ∈ ∅, st[r -- fs '] = refval(r0), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ junkref(str, r, st), cyclic(str, r, st), has_reffield((r ' + refs0) .last, st), dups(refs0), r ∈ refs0

Rule argument

[speclemmaarg: ,refsset = refsset0 ↔ (∀ refs. refs ∈ refsset ↔ refs ∈ refsset0) ,[refsset0, refsset] → [∅, validrefset(str, r, st)] ,F ,set-basic ,reflistset ,Extension ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (∅, validrefset(str, r, st))]]