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Theorem notin

⊦ ¬ a ∈ x → #oc(a, x) = 0

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: del-04, delapp, diff, filter, in, in-01, nodups, oc-dups, oc-zero, ocnodups, ocnodups-01, perm-all, perm-del-01, perm-put-del1, size-perm, subdel-02, subdel-03, subrec, subsize,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 4
Used lemmas: one-01, ocappend, oc-e,
Used spec theorems:
- Used simplifier rules:
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/add-base
  - list/in-06
  - list/a
  - list/c