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Proof step 37 from proof maxpath-object (previous step)

maxpath(str, r0, st) = 1 + # refs1, st[r -- fs '] = refval(r0), maxpath(str, r, st) = 2 + # refs, validrefs(str, r ' + r0 ' + refs1, st[r -- _type] .type, st), validrefs(str, r0 ' + refs1, st[r0 -- _type] .type, st), maxpath(str, r, st) ≤ maxpath(str, r0, st), validrefs(str, r ' + refs + r1 ', st[r -- _type] .type, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), # refs < # refs1, is_valid_ref(str, r0, st) ⊦ validrefset(str, r, st) = ∅, # validrefset(str, r, st) = 0, r = r1, validrefset(str, r0, st) = ∅, # validrefset(str, r0, st) = 0, refs1 = [], junkref(str, r, st), cyclic(str, r, st), has_reffield(r1, st), r ∈ refs, r1 ∈ refs, dups(refs), r0 ∈ refs1, dups(refs1), has_reffield(refs1 .last, st), r ≠ r0 ∧ ¬ r ∈ refs1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: , cyclic(str, r, st) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st)) ,[st, r, str] → [st, r, str] ,F ,cyclic , ,cyclic-def-simple ]

Additional information

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