Mathlib Map

Theorems · Theorem · group theory

Function.Injective.isLeftCancelAdd

∀ {M₁ : Type u_1} {M₂ : Type u_2} [inst : Add M₁] [inst_1 : Add M₂] [IsLeftCancelAdd M₂] (f : M₁ → M₂),
  Function.Injective f → (∀ (x y : M₁), f (x + y) = f x + f y) → IsLeftCancelAdd M₁

A type has left-cancellative addition, if it admits an injective map that preserves + to another type with left-cancellative addition.

Defined in
Mathlib.Algebra.Group.InjSurj
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
AddAddIsLeftCancelAdd
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Around this declaration

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

Function.Injective.isCancelAdd · cited by 2Injective.isCancelAddEquiv.isLeftCancelAdd · cited by 0Equiv.isLeftCancelAddFunLike.isLeftCancelAdd · cited by 0FunLike.isLeftCancelAddIsLeftCancelAdd · cited by 72IsLeftCancelAddadd_left_cancel · cited by 29add_left_cancelInjective.isLeftCancelAddCITED BYCITES

Cites2

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Cited by3

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