Theorems · Theorem · order theory
sup_bot_eq
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderBot α] (a : α), a ⊔ ⊥ = a- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- SemilatticeSupOrderBot
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.
- Bot.botstatement · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- bot_leproof · cited by 306
- sup_of_le_leftproof · cited by 218
Cited by31
Results whose statement or proof uses this declaration.
- sdiff_botproof · cited by 13
- Submodule.le_of_le_smul_of_le_jacobson_botproof · cited by 9
- sup_sdiff_right_selfproof · cited by 6
- Disjoint.sup_sdiff_cancel_rightproof · cited by 5
- sdiff_inf_self_rightproof · cited by 4
- symmDiff_botproof · cited by 4
- eq_top_of_isCompl_botproof · cited by 4
- Finset.sup'_inductionproof · cited by 3
- MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
- Codisjoint.le_of_disjointproof · cited by 2
- MeasureTheory.IsSetSemiring.mem_supClosure_iffproof · cited by 2
- symmDiff_of_geproof · cited by 2