Mathlib Map

Theorems · Definition · order theory

WithBot.ofDual

{α : Type u_1} → WithBot αᵒᵈ ≃ WithTop α

WithBot.ofDual is the equivalence sending ⊥ to ⊤ and any a : αᵒᵈ to ofDual a : α. See WithBot.ofDualTopEquiv for the related order-iso.

Defined in
Mathlib.Order.WithBot
Cited by
18 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

WithBot.coe_toDualTopEquiv · cited by 1WithBot.coe_toDualTopEquivWithBot.ofDual_lt_iff · cited by 0WithBot.ofDual_lt_iffWithBot.ofDual_lt_ofDual_iff · cited by 0WithBot.ofDual_lt_ofDual_…WithBot.lt_ofDual_iff · cited by 0WithBot.lt_ofDual_iffWithBot.coe_toDualTopEquiv_eq · cited by 0WithBot.coe_toDualTopEqui…WithBot.ofDual_map · cited by 0WithBot.ofDual_mapWithBot.ofDual_symm · cited by 0WithBot.ofDual_symmWithBot.map_ofDual · cited by 0WithBot.map_ofDualWithTop.toDual_le_iff · cited by 0WithTop.toDual_le_iffWithTop.toDual_lt_iff · cited by 0WithTop.toDual_lt_iffWithTop.le_toDual_iff · cited by 0WithTop.le_toDual_iffWithTop.toDual_symm · cited by 0WithTop.toDual_symmWithBot.le_ofDual_iff · cited by 0WithBot.le_ofDual_iffWithTop.lt_toDual_iff · cited by 0WithTop.lt_toDual_iffWithBot.ofDual_apply_coe · cited by 0WithBot.ofDual_apply_coeEquiv · cited by 8337EquivWithTop · cited by 3754WithTopWithBot · cited by 1498WithBotOrderDual · cited by 927OrderDualEquiv.refl · cited by 274Equiv.reflWithBot.ofDualCITED BYCITES

Cites5

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

Cited by18

Results whose statement or proof uses this declaration.