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Structures · Algebra

AddCancelMonoid

An additive monoid in which addition is cancellative on both sides. Main examples are and groups. This is the right typeclass for many sum lemmas, as having a zero is useful to define the sum over the empty set, so AddRightCancelMonoid is not enough.

Defined in
Mathlib.Algebra.Group.Defs
Shape
One type argument

Extends2

Extended by2

Forgetful instances

Provided automatically by

Concrete types that are instances10

  • Matrix
  • DomAddAct
  • FreeAddMonoid
  • DyckWord
  • Prod
  • OrderDual
  • ULift
  • Lex
  • AddOpposite
  • Colex

How is a type an instance?

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Assumed by34

Ancestors21