Mathlib Map

Theorems · Theorem · order theory

OrderEmbedding.ofIsEmpty_apply

∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] [inst_2 : IsEmpty α] (a : α),
  OrderEmbedding.ofIsEmpty a = isEmptyElim a
Defined in
Mathlib.Order.Hom.Basic
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses no axioms
Assumes
PreorderPreorderIsEmpty
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Around this declaration

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

OrderEmbedding.birkhoffSet_inf · cited by 1OrderEmbedding.birkhoffSe…OrderEmbedding.birkhoffSet_sup · cited by 1OrderEmbedding.birkhoffSe…DFunLike.coe · cited by 62936DFunLike.coePreorder · cited by 7952PreorderIsEmpty · cited by 759IsEmptyRelEmbedding · cited by 281RelEmbeddingisEmptyElim · cited by 59isEmptyElimOrderEmbedding.ofIsEmpty · cited by 6OrderEmbedding.ofIsEmptyOrderEmbedding.ofIsEmpty_applyCITED BYCITES

Cites6

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

Cited by2

Results whose statement or proof uses this declaration.