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Theorems · Theorem · order theory

antisymm_of

∀ {α : Sort u_1} (r : α → α → Prop) [Std.Antisymm r] {a b : α}, r a b → r b a → a = b

A version of antisymm with r explicit. This lemma matches the lemmas from lean core in Init.Algebra.Classes, but is missing there.

Defined in
Mathlib.Order.Defs.Unbundled
Cited by
2 results in Mathlib
Foundations
Depth 3 from the axioms · uses no axioms
Assumes
Std.Antisymm
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Function.Injective.antisymm_onFun · cited by 1Injective.antisymm_onFunOrder.Preimage.antisymm · cited by 1Preimage.antisymmantisymm · cited by 13antisymmantisymm_ofCITED BYCITES

Cites1

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.