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Proof step 14 from proof pathex-def-nodups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]