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Theorems · Theorem · order theory

WithBot.denselyOrdered_iff

∀ {α : Type u_1} [inst : LT α] [NoMinOrder α], DenselyOrdered (WithBot α) ↔ DenselyOrdered α
Defined in
Mathlib.Order.WithBot
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses propext, Quot.sound
Assumes
LTNoMinOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithZero.denselyOrdered_iff · cited by 0WithZero.denselyOrdered_i…Bot.bot · cited by 4720Bot.botWithBot · cited by 1498WithBotWithBot.some · cited by 541WithBot.someDenselyOrdered · cited by 471DenselyOrderedNoMinOrder · cited by 247NoMinOrderexists_between · cited by 102exists_betweenWithBot.recBotCoe · cited by 101WithBot.recBotCoeWithBot.coe_lt_coe · cited by 55WithBot.coe_lt_coeDenselyOrdered.dense · cited by 8DenselyOrdered.denseWithBot.denselyOrdered_iffCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.