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Theorem lastn-neq-01

⊦ n ≤ # x ∧ a ∈ y ∧ ¬ a ∈ x → lastn(n, x) ≠ b ' + y

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: lastn-neq-04,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 5
Used lemmas: lastN-in-01, lastN-rec, lastN-zero,
Used spec theorems:
- Used simplifier rules:
  - list/app-02-ant
  - list/e
  - list-data/l
  - nat-basic1/f
  - nat/succ-01
  - nat-basic2/succ
  - list/in-rec
  - list/Last
  - list/e-02
  - list/a
  - list/len
  - list/len-02
  - nat-basic2/s
  - nat-basic2/a
  - nat-basic2/c
  - list/in-append
  - list/in-17
  - nat/lels
  - list/inapp-13
  - list/in-15
  - list/in-14
  - list-last/last-elim