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Theorems · Theorem · order theory

MulLECancellable.Injective

∀ {α : Type u_1} [inst : Mul α] [inst_1 : PartialOrder α] {a : α},
  MulLECancellable a → Function.Injective fun x => a * x
Defined in
Mathlib.Algebra.Order.Monoid.Unbundled.Basic
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
MulPartialOrder
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Around this declaration

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

MulLECancellable.injective_left · cited by 1MulLECancellable.injectiv…MulLECancellable.inj · cited by 0MulLECancellable.injMulLECancellable.isLeftRegular · cited by 0MulLECancellable.isLeftRe…PartialOrder · cited by 6410PartialOrderle_antisymm · cited by 2068le_antisymmEq.le · cited by 605Eq.leEq.ge · cited by 375Eq.geMulLECancellable · cited by 20MulLECancellableMulLECancellable.InjectiveCITED BYCITES

Cites5

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Cited by3

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