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Proof step 25 from proof cyclic-def-shortest (previous step)

⊦ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[r -- _type] .type, st)) ↔ (∃ refs, r0. ¬ dups(refs) ∧ r0 ∈ refs ∧ refs .first = r ∧ validrefs(str, refs + r0 ', st[refs .first -- _type] .type, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
⊦ (∃ refs. dups(refs) ∧ refs .first = r ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)) ↔ (∃ refs, r0. ¬ dups(refs) ∧ r0 ∈ refs ∧ refs .first = r ∧ validrefs(str, refs + r0 ', st[refs .first -- _type] .type, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]