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Theorem firstN-dups-04

⊦ n ≤ # x ∧ ¬ dups(x) → ¬ dups(firstn(n, x))

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: firstN-dups-02, firstN-dups-03, firstN-dups-05,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 6
Used lemmas: firstN-in, firstN-rec, firstN-zero,
Used spec theorems:
- Used simplifier rules:
  - list-dup/e-01
  - list-data/l
  - nat-basic1/f
  - nat/succ-01
  - list-data/elim-list-c
  - nat/lels
  - list-dup/rec
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/s
  - nat-basic2/succ
  - list/len-05
  - list/a
  - list/e-01
  - list/c