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Proof step 19 from proof pathex-def-nodups (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 18:
validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ refs1 = [], r = (r ' + refs1) .last, ∃ refs. refs ≠ [] ∧ refs .first = r ∧ refs .last = (refs .first ' + refs1) .last ∧ ¬ dups(refs) ∧ validrefs(str, refs, st[refs .first -- _type] .type, st)

Rule argument

[fma-arg: refs1 = []]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' .last = r])], [EXTRAFMAS : (refs1 = [])]]