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Theorem allls-in

⊦ n ∈ ix ∧ all<(ix, n0) → (n0 ≤ n ↔ false)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 4
Used lemmas: allls-rec,
Used spec theorems:
- Used simplifier rules:
  - list/indexseq/in-empty
  - nat-basic1/f
  - nat/fle
  - nat/le-ls-simp
  - list/indexseq/a
  - list/indexseq/in-17
  - list/indexseq/in-append
  - list/indexseq/c