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Theorems · Theorem · order theory

Subtype.mk_bot

∀ {α : Type u} {p : α → Prop} [inst : PartialOrder α] [inst_1 : OrderBot α] [inst_2 : OrderBot (Subtype p)]
  (hbot : p ⊥), ⟨⊥, hbot⟩ = ⊥
Defined in
Mathlib.Order.BoundedOrder.Basic
Cited by
4 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
PartialOrderOrderBotOrderBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ComplementedLattice.isStronglyAtomic · cited by 2ComplementedLattice.isStr…Subtype.coe_bot · cited by 2Subtype.coe_botfactor_orderIso_map_one_eq_bot · cited by 1factor_orderIso_map_one_e…Complementeds.mk_bot · cited by 0Complementeds.mk_botPartialOrder · cited by 6410PartialOrderBot.bot · cited by 4720Bot.botOrderBot · cited by 1055OrderBotbot_le · cited by 306bot_lele_bot_iff · cited by 116le_bot_iffSubtype.coe_le_coe · cited by 20Subtype.coe_le_coeSubtype.mk_botCITED BYCITES

Cites6

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Cited by4

Results whose statement or proof uses this declaration.