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Theorem cyclic-def-shortest

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: cyclic-put-badarrayfield, cyclic-put-badclassfield, cyclic-put-nopathex, cyclic-putbyte-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 12
Proof steps: 25
Used lemmas: validrefs-prefix, cyclic-def-simple,
Used spec theorems:
- Used simplifier rules:
  - list/references/len
  - list/references/len-02
  - nat-basic2/s
  - nat-basic1/ref-1
  - nat-basic2/a
  - nat-basic2/c
  - list-dup/references/dups-cons
  - list-dup/references/f
  - list/references/in-17
  - list/references/in-append
  - list/references/e-02
  - list-last/references/last-elim
  - list-last/references/butlast-last
  - list/references/c-08
  - list/references/in-06
  - list/references/app
  - list/references/in-empty
  - list-dup/references/rec
  - list/references/a
  - list/references/e-01
  - list/references/c
  - list-dup/references/e-01
  - list-data/references/elim-list-c