Theorems · Inductive type · order theory
Preorder
Type u_2 → Type u_2
A preorder is a reflexive, transitive relation ≤.
In a preorder, a < b means a ≤ b ∧ ¬b ≤ a, and < is defined this way by default.
You can override this definition to set a better def-eq.
- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 7,952 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
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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 by9,091
Results whose statement or proof uses this declaration.
- LE.le.transstatement · cited by 3,151
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- le_rflstatement and proof · cited by 1,558
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- Monotonestatement and proof · cited by 1,397
- OrderTopologystatement · cited by 1,355
- Set.Ioostatement and proof · cited by 1,214
Showing the 200 most cited of 9,091.