Theorems · Theorem · order theory
InfIrred.ne_top
∀ {α : Type u_2} [inst : SemilatticeInf α] {a : α} [inst_1 : OrderTop α], InfIrred a → a ≠ ⊤- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- InfIrredstatement and proof · cited by 27
- not_infIrred_topproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- UpperSet.infIrred_iff_of_finiteproof · cited by 1
- InfIrred.isPrimaryproof · cited by 1