Theorems · Definition · order theory
SupPrime
{α : Type u_2} → [SemilatticeSup α] → α → PropA sup-prime element is a non-bottom element which isn't less than the supremum of anything smaller.
- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- SemilatticeSup
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.
- SemilatticeSupstatement and proof · cited by 785
- IsMinproof · cited by 277
Cited by19
Results whose statement or proof uses this declaration.
- SupPrime.le_supstatement and proof · cited by 1
- SupPrime.ne_botstatement and proof · cited by 1
- not_supPrimestatement · cited by 1
- not_supPrime_botstatement · cited by 1
- SupPrime.supIrredstatement · cited by 1
- IsMin.not_supPrimestatement and proof · cited by 1
- supPrime_iff_supIrredstatement · cited by 1
- supPrime_ofDualstatement · cited by 1
- supPrime_toDualstatement · cited by 1
- infPrime_ofDualstatement · cited by 1
- infPrime_toDualstatement · cited by 1
- SupPrime.le_finset_supstatement and proof · cited by 1