Theorems · Theorem · order theory
Disjoint.eq_bot
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] {a b : α}, Disjoint a b → a ⊓ b = ⊥- Defined in
- Mathlib.Order.Disjoint
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SemilatticeInfOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement · cited by 4,720
- Disjointstatement · cited by 2,201
- OrderBotstatement and proof · cited by 1,055
- SemilatticeInfstatement and proof · cited by 634
- bot_uniqueproof · cited by 57
- Disjoint.le_botproof · cited by 52
Cited by52
Results whose statement or proof uses this declaration.
- Disjoint.sdiff_eq_leftproof · cited by 19
- Disjoint.inter_eqproof · cited by 18
- Filter.Tendsto.not_tendstoproof · cited by 14
- IsCompl.inf_eq_botproof · cited by 11
- regularSpace_TFAEproof · cited by 6
- LieAlgebra.IsKilling.root_apply_cartanEquivDual_symm_ne_zeroproof · cited by 4
- Module.End.independent_genEigenspaceproof · cited by 4
- Submodule.finrank_add_inf_finrank_orthogonalproof · cited by 3
- Disjoint.disjoint_sup_right_of_disjoint_sup_leftproof · cited by 3
- Disjoint.le_of_codisjointproof · cited by 3
- Disjoint.le_symmDiff_sup_symmDiff_leftproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2