Theorems · Definition · order theory
InfPrime
{α : Type u_2} → [SemilatticeInf α] → α → PropAn inf-prime element is a non-top element which isn't bigger than the infimum of anything bigger.
- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 26 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 by26
Results whose statement or proof uses this declaration.
- PrimitiveSpectrum.hull_finsetInfstatement and proof · cited by 2
- PrimitiveSpectrum.isClosed_iffstatement and proof · cited by 2
- IsMax.not_infPrimestatement and proof · cited by 1
- infPrime_iff_infIrredstatement · cited by 1
- infPrime_ofDualstatement · cited by 1
- infPrime_toDualstatement · cited by 1
- InfPrime.infIrredstatement · cited by 1
- PrimitiveSpectrum.hull_infstatement and proof · cited by 1
- PrimitiveSpectrum.hull_kernel_of_isClosedstatement and proof · cited by 1
- not_infPrime_topstatement · cited by 1
- PrimitiveSpectrum.isOpen_iffstatement and proof · cited by 1
- PrimitiveSpectrum.isTopologicalBasis_relativeLowerstatement and proof · cited by 1