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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: s, ls,
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: 2
Proof steps: 9
Used lemmas: elim-firstn-restn, firstN-rec-01, firstN-zero,
Used spec theorems:
- Used simplifier rules:
  - list-data/size-nil
  - nat/lez-01
  - list/in-empty
  - list/a
  - list/in-06
  - list/c
  - nat-basic/succ
  - list/len-05
  - nat/lez
  - list/in-01
  - nat/pred-03
  - nat/elim-pred-c
  - nat-basic/c
  - nat-basic/a
  - nat/lep-02
  - nat-basic/oz
  - list/len
  - nat/lep
  - list/in-11