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Theorem precedes-trans

⊦ precedes(n, n0, x) ∧ precedes(n0, n1, x) → (¬ precedes(n, n1, x) ↔ false)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: ascsubseq-first-notin-rest, ascsubseq-nodups, ascsubseq-rest-notprec-first, precedes-ascsubseq-2-h,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 6
Used lemmas: precedes-def,
Used spec theorems:
- Used simplifier rules:
  - list-data/l
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/succ
  - nat-basic1/f
  - oelem/transitivity
  - oelem/indexseq/transitivity
  - nat-basic1/lf