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Theorems · Theorem · order theory

SupIrred.ne_bot

∀ {α : Type u_2} [inst : SemilatticeSup α] {a : α} [inst_1 : OrderBot α], SupIrred a → a ≠ ⊥
Defined in
Mathlib.Order.Irreducible
Cited by
2 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
SemilatticeSupOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SupIrred.finset_sup_eq · cited by 1SupIrred.finset_sup_eqLowerSet.supIrred_iff_of_finite · cited by 1LowerSet.supIrred_iff_of_…Bot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotSemilatticeSup · cited by 785SemilatticeSupSupIrred · cited by 34SupIrrednot_supIrred_bot · cited by 1not_supIrred_botSupIrred.ne_botCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.