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Theorem firstN-in

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

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: firstN-dups-04, firstN-in-01, firstN-in-02, firstN-in-03, firstN-in-04, firstn-restn-in,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 2
Used lemmas: elim-firstn-restn,
Used spec theorems:
- Used simplifier rules:
  - list/len
  - list/a
  - nat/lep
  - nat-basic2/a
  - nat-basic2/c
  - list/in-11