Theorems · Definition · order theory
Pi.Lex
{ι : Type u_1} →
{β : ι → Type u_2} → (ι → ι → Prop) → ({i : ι} → β i → β i → Prop) → ((i : ι) → β i) → ((i : ι) → β i) → PropThe lexicographic relation on Π i : ι, β i, where ι is ordered by r,
and each β i is ordered by s.
The < relation on Lex (∀ i, β i) is Pi.Lex (· < ·) (· < ·), while the < relation on
Colex (∀ i, β i) is Pi.Lex (· > ·) (· < ·).
- Defined in
- Mathlib.Order.PiLex
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by13
Results whose statement or proof uses this declaration.
- DFinsupp.Lexproof · cited by 14
- Finsupp.Lexproof · cited by 11
- Pi.lex_iff_of_uniquestatement · cited by 4
- Pi.Lex.wellFoundedstatement and proof · cited by 2
- Pi.trichotomous_lexstatement and proof · cited by 1
- DFinsupp.lex_lt_of_ltstatement · cited by 1
- Pi.isTrichotomous_lexstatement · cited by 0
- Finsupp.lex_lt_of_ltstatement · cited by 0
- Pi.lex_eq_dfinsupp_lexstatement · cited by 0
- Pi.lex_eq_finsupp_lexstatement · cited by 0
- Pi.lex_lt_of_ltstatement · cited by 0
- Fin.pi_lex_lt_cons_consstatement · cited by 0