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Proof step 13 from proof pathex-def-nodups (previous step)

validrefs(str, r ' + refs1, st[r -- _type] .type, st), r ∈ refs1 ⊦ refs1 = [], r = refs1 .last, dups(refs1), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = refs1 .last ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1))
Proof step 12:
validrefs(str, r ' + refs1, st[r -- _type] .type, st), ∃ refs0, refs2. refs1 = refs0 + (r + refs2) ⊦ refs1 = [], r = refs1 .last, dups(refs1), ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = refs1 .last ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Rule argument

[speclemmaarg: ,r ∈ refs ↔ (∃ refs0, refs1. refs = refs0 + (r + refs1)) ,[refs, r] → [refs1, r] ,F ,list ,references ,In ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (refs1, r)]]