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Theorems · Theorem · order theory

Monotone.strictMono_iff_injective

∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : PartialOrder β] {f : α → β},
  Monotone f → (StrictMono f ↔ Function.Injective f)
Defined in
Mathlib.Order.Monotone.Basic
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
LinearOrderPartialOrder
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Around this declaration

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

CircleDeg1Lift.strictMono_iff_injective · cited by 1CircleDeg1Lift.strictMono…LinearOrder · cited by 8572LinearOrderPartialOrder · cited by 6410PartialOrderMonotone · cited by 1397MonotoneStrictMono · cited by 706StrictMonoStrictMono.injective · cited by 94StrictMono.injectiveMonotone.strictMono_of_injective · cited by 22Monotone.strictMono_of_in…Monotone.strictMono_iff_injec…CITED BYCITES

Cites6

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Cited by1

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