Theorems · Theorem · order theory
bot_inf_eq
∀ {α : Type u_1} [inst : SemilatticeInf α] [inst_1 : OrderBot α] (a : α), ⊥ ⊓ a = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Lattice
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
- Assumes
- SemilatticeInfOrderBot
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
- SemilatticeInfstatement and proof · cited by 634
- bot_leproof · cited by 306
- inf_of_le_leftproof · cited by 186
Cited by11
Results whose statement or proof uses this declaration.
- sdiff_sdiff_rightproof · cited by 4
- Submodule.finrank_add_inf_finrank_orthogonalproof · cited by 3
- IsCompl.sup_infproof · cited by 2
- inf_sdiffproof · cited by 2
- isCompl_bot_topproof · cited by 2
- Subgroup.subgroupOf_eq_botproof · cited by 1
- AddSubgroup.addSubgroupOf_eq_botproof · cited by 1
- Interval.coe_infproof · cited by 1
- min_bot_leftproof · cited by 0
- rank_add_rank_splitproof · cited by 0
- Coheyting.boundary_botproof · cited by 0