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Theorem nodups-butlastn

⊦ ¬ dups(x) ∧ n ≤ # x → (dups(butlastn(n, x)) ↔ false)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 8
Proof steps: 23
Used lemmas: lb, blastN-all-01, b, bapp, butlastN-rec, blastN-rec-01, butlastN-base,
Used spec theorems:
- Used simplifier rules:
  - nat-basic1/ref-1
  - nat-basic2/s
  - nat/lep-02
  - nat-basic2/oz
  - nat-basic1/lf-01
  - nat-basic1/f
  - nat/eqle-one
  - nat/les
  - list-dup/e-01
  - list-dup/rec
  - nat/lez-01
  - list/in-06
  - list/c
  - list-data/size-01
  - list/app
  - list/len-05
  - nat-basic2/succ
  - nat/lels-01
  - nat-basic1/one-01
  - list-data/l
  - nat/eq-02
  - nat-basic2/c
  - nat-basic2/a
  - list/in-empty
  - list/a
  - list/in-01