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Proof step 3 from proof cyclic-def-object (previous step)

is_obj(str, r, st), validrefs(str, r ' + refs1, mkclasstype(`java.lang.Object' .class), st) ⊦ ∃ refs0. dups(refs0) ∧ refs0 .first = r ∧ validrefs(str, refs0, st[refs0 .first -- _type] .type, st), ¬ r ∈ refs1 ∧ ¬ dups(refs1)

User applied rule exists right

And obtained the following new goals

Proof step 2:
⊦ ¬ validrefs(str, r ' + refs, st[r -- _type] .type, st) → ¬ validrefs(str, r ' + refs, ty, st)

Rule argument

[EXRARG : pos: right 1, [extquanttermlist: (r ' + refs1) abort:F , discard:T , computed:F ]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(r ' + refs) ↔ dups(refs) ∨ r ∈ refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ (r ' + refs) .first = r])], [EXTRATERMS : (r ' + refs1)]]