Theorems · Definition · order theory
InfIrred
{α : Type u_2} → [SemilatticeInf α] → α → PropAn inf-irreducible element is a non-top element which isn't the infimum of anything bigger.
- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SemilatticeInfstatement and proof · cited by 634
- IsMaxproof · cited by 372
Cited by29
Results whose statement or proof uses this declaration.
- UpperSet.infIrred_Icistatement · cited by 4
- OrderIso.infIrredUpperSetstatement · cited by 3
- OrderEmbedding.infIrredUpperSetstatement · cited by 2
- InfIrred.ne_topstatement and proof · cited by 2
- exists_infIrred_decompositionstatement · cited by 1
- not_infIrred_topstatement · cited by 1
- Submodule.isLaskerproof · cited by 1
- InfPrime.infIrredstatement · cited by 1
- UpperSet.infIrred_iff_of_finitestatement and proof · cited by 1
- supIrred_ofDualstatement · cited by 1
- supIrred_toDualstatement · cited by 1
- infIrred_ofDualstatement · cited by 1