Theorems · Theorem · order theory
Antitone.strictAnti_iff_injective
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : PartialOrder β] {f : α → β},
Antitone f → (StrictAnti f ↔ Function.Injective f)- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderPartialOrder
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- PartialOrderstatement and proof · cited by 6,410
- Antitonestatement and proof · cited by 563
- StrictAntistatement and proof · cited by 204
- StrictAnti.injectiveproof · cited by 12
- Antitone.strictAnti_of_injectiveproof · cited by 2
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