Antisymmetrization
π Source: Mathlib/Order/Antisymmetrization.lean
Statistics
AntisymmRel
Definitions
| Name | Category | Theorems |
|---|---|---|
decidableRel π | CompOp | β |
setoid π | CompOp |
Theorems
Antisymmetrization
Definitions
| Name | Category | Theorems |
|---|---|---|
prodEquiv π | CompOp |
Theorems
Eq
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
antisymmRel π | mathematical | β | AntisymmRel | β | AntisymmRel.of_eq |
LE.le
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
lt_or_antisymmRel π | mathematical | Preorder.toLE | Preorder.toLTAntisymmRel | β | le_iff_lt_or_antisymmRel |
trans_antisymmRel π | β | Preorder.toLEAntisymmRel | β | β | le_of_le_of_antisymmRel |
LT.lt
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
not_antisymmRel π | mathematical | Preorder.toLT | AntisymmRelPreorder.toLE | β | not_antisymmRel_of_lt |
not_antisymmRel_symm π | mathematical | Preorder.toLT | AntisymmRelPreorder.toLE | β | not_antisymmRel_of_gt |
symmGen π | mathematical | Preorder.toLT | Relation.SymmGenPreorder.toLE | β | Relation.SymmGen.of_lt |
symmGen_symm π | mathematical | Preorder.toLT | Relation.SymmGenPreorder.toLE | β | Relation.SymmGen.of_gt |
trans_antisymmRel π | β | Preorder.toLTAntisymmRelPreorder.toLE | β | β | lt_of_lt_of_antisymmRel |
Mathlib.Tactic.GCongr
Definitions
| Name | Category | Theorems |
|---|---|---|
exactAntisymmRelLeft π | CompOp | β |
exactAntisymmRelRight π | CompOp | β |
Mathlib.Tactic.GCongr.AntisymmRel
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
left π | β | AntisymmRel | β | β | β |
right π | β | AntisymmRel | β | β | β |
OrderEmbedding
Definitions
| Name | Category | Theorems |
|---|---|---|
ofAntisymmetrization π | CompOp |
Theorems
| Name | Kind | Assumes | Proves | Validates | Depends On |
|---|---|---|---|---|---|
ofAntisymmetrization_apply π | mathematical | β | DFunLike.coeRelEmbeddingAntisymmetrizationPreorder.toLEinstIsPreorderLePartialOrder.toPreorderinstPartialOrderAntisymmetrizationRelEmbedding.instFunLikeofAntisymmetrizationofAntisymmetrization | β | instIsPreorderLe |
OrderHom
Definitions
| Name | Category | Theorems |
|---|---|---|
antisymmetrization π | CompOp |
Theorems
OrderIso
Definitions
| Name | Category | Theorems |
|---|---|---|
dualAntisymmetrization π | CompOp |
Theorems
Relation.SymmGen
Theorems
(root)
Definitions
Theorems
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