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Theorem ocs-dups-ex

⊦ dups(x) ↔ (∃ a. a ∈ x ∧ #oc(a, x) > 1)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 11
Used lemmas: oc-zero, oc-e, one, ocappend, in-05,
Used spec theorems:
- list-dup/dups
Used simplifier rules:
- nat-basic1/one
- nat/gr-def
- list/in-01
- list/in-append
- nat/add-num-03
- list/in-empty
- list-dup/rec
- list/in-rec
- nat-basic2/c
- nat-basic2/a
- list/in-17
- nat-basic2/one
- list/a
- list/c