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Proof step 16 from proof pathex-def-nodups (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
validrefs(str, r ' + refs1, st[r -- _type] .type, st) ⊦ 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)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ dups(r ' + refs) ↔ ¬ ¬ (r ∈ refs ∨ dups(refs))], [CSIMPSEQ : ⊦ refs ≠ [] → (r ' + refs) .last = refs .last], [CSIMPSEQ : ⊦ (r ' + refs) .first = r], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ' ≠ []], [CSIMPSEQ : ⊦ ¬ refs + refs0 ≠ [] ↔ refs = [] ∧ refs0 = []])]]