Theorems · Definition · order theory
PartialOrder.ofSetLike
(A : Type u_1) → (B : Type u_2) → [SetLike A B] → PartialOrder A
The partial order induced from a SetLike instance by inclusion.
A partial order defined as .ofSetLike will automatically make available an instance
of IsConcreteLE.
- Defined in
- Mathlib.Data.SetLike.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- SetLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coeproof · cited by 8,199
- PartialOrderstatement and proof · cited by 6,410
- SetLikestatement and proof · cited by 1,084
- SetLike.coe_injectiveproof · cited by 374
- PartialOrder.le_antisymmproof · cited by 1
- PartialOrder.liftproof · cited by 1
- LE.ofSetLikeproof · cited by 0
Cited by0
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