Theorems · Definition · order theory
DedekindCut.left
{α : Type u_1} → [inst : Preorder α] → DedekindCut α → Set αThe left set of a Dedekind cut. This is an alias for Concept.extent.
- Defined in
- Mathlib.Order.Completion
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Concept.extentproof · cited by 52
- DedekindCutstatement and proof · cited by 27
Cited by17
Results whose statement or proof uses this declaration.
- DedekindCut.factorEmbeddingproof · cited by 3
- DedekindCut.extstatement and proof · cited by 3
- DedekindCut.factorEmbedding_applystatement · cited by 2
- DedekindCut.factorEmbedding_principalproof · cited by 1
- DedekindCut.left_principalstatement · cited by 1
- DedekindCut.lowerBounds_rightstatement · cited by 1
- DedekindCut.principal_le_iffstatement and proof · cited by 1
- DedekindCut.upperBounds_leftstatement · cited by 1
- DedekindCut.continuous_principalproof · cited by 1
- DedekindCut.ext_iffstatement and proof · cited by 0
- DedekindCut.image_left_subset_lowerBoundsstatement and proof · cited by 0
- DedekindCut.image_right_subset_upperBoundsstatement and proof · cited by 0