Theorems · Theorem · order theory
bot_sup_eq
∀ {α : Type u_1} [inst : SemilatticeSup α] [inst_1 : OrderBot α] (a : α), ⊥ ⊔ a = a- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 32 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_rightproof · cited by 143
Cited by32
Results whose statement or proof uses this declaration.
- sdiff_sdiff_right_selfproof · cited by 20
- sdiff_eq_bot_iffproof · cited by 10
- Submodule.orthogonal_eq_bot_iffproof · cited by 7
- inf_sdiff_self_rightproof · cited by 6
- sdiff_inf_self_leftproof · cited by 5
- symmDiff_of_leproof · cited by 4
- sdiff_sdiff_rightproof · cited by 4
- inf_sdiff_distrib_leftproof · cited by 3
- Disjoint.disjoint_sup_right_of_disjoint_sup_leftproof · cited by 3
- Disjoint.le_of_codisjointproof · cited by 3
- Finset.sup'_inductionproof · cited by 3
- PhragmenLindelof.right_half_plane_of_tendsto_zero_on_realproof · cited by 2