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Proof step 34 from proof cyclic-def-object (previous step)

is_obj(str, r, st) ⊦ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st)) ↔ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st))

User applied rule case distinction

And obtained the following new goals

Proof step 6:
∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st), is_obj(str, r, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)
Proof step 33:
∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st), is_obj(str, r, st) ⊦ ∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, mkclasstype(`java.lang.Object' .class), st)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]