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Theorem allls-one

⊦ all<(x, m, m + 1, a) ↔ m ≥ # x ∨ x[m] < a

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 7
Used lemmas: allls-range-def,
Used spec theorems:
- Used simplifier rules:
  - nat/ge
  - nat-basic/c
  - nat-basic/a
  - nat-basic/s-04
  - nat/lels
  - nat/anti
  - nat-basic/f
  - nat-basic/lf-02
  - nat/fle
  - nat/let
  - list-data/l
  - nat/le-ls-simp
  - nat/ls-le-simp
  - nat/le-def
  - nat/ler
  - nat-basic/refl-nat