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Theorem ole-last

⊦ ordered≤(x + a ') → (ordered≤(x + a ' + b ') ↔ ¬ b < a)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: ole-last-01,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 22
Used lemmas: le-o, le-r, ole-in, ole-rec, app-02, app, app-01, cons-02, ole-two,
Used spec theorems:
- Used simplifier rules:
  - list/app-02-ant
  - list/e
  - list-data/elim-list-c
  - list/ni
  - oelem/nen
  - list/app
  - list/c-05
  - list/in-empty
  - list/Nil
  - oelem/nnn
  - list/in-17
  - list/in-append
  - list/in-12
  - oelem/irreflexivity
  - list/c-08
  - list/first-02
  - list/e-01
  - list/c-07
  - list/in-11
  - list/in-01
  - list/in-15
  - oelem/ls-le
  - list-last/lin-01
  - list/inapp-10
  - list-last/lapp-04
  - oelem/sls
  - list-last/last-elim
  - list/c
  - list/in-rec
  - oelem/nll
  - list/in-14
  - list/e-02
  - list/a
  - list/app-06