Theorems · Theorem · order theory
Concept.mem_extent_of_rel_extent
∀ {α : Type u_2} {r' : α → α → Prop} {c' : Concept α α r'} [IsTrans α r'] {x y : α},
r' y x → x ∈ c'.extent → y ∈ c'.extent- Defined in
- Mathlib.Order.Concept
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- IsTrans
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- IsTransstatement and proof · cited by 157
- transproof · cited by 111
- Conceptstatement and proof · cited by 78
- Concept.extentstatement and proof · cited by 52
- Concept.intentproof · cited by 51
- Concept.lowerPolar_intentproof · cited by 8
- Concept.rel_extent_intentproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- DedekindCut.principal_le_iffproof · cited by 1
- Concept.codisjoint_extent_intentproof · cited by 1
- Concept.isLowerSet_extent_leproof · cited by 0
- Concept.isLowerSet_extent_ltproof · cited by 0