Theorems · Inductive type · group theory
AddCancelMonoid
Type u → Type u
An additive monoid in which addition is cancellative on both sides.
Main examples are ℕ 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
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by31
Results whose statement or proof uses this declaration.
- Finset.HasAntidiagonal.antidiagonal_congrstatement and proof · cited by 4
- MeasureTheory.FinMeasAdditive.map_empty_eq_zerostatement and proof · cited by 3
- AddCancelMonoid.extstatement and proof · cited by 2
- AddCancelMonoid.casesOnstatement and proof · cited by 1
- Measurable.add_simpleFuncstatement and proof · cited by 1
- AddCancelMonoid.toAddLeftCancelMonoid_injectivestatement and proof · cited by 1
- Measurable.add_stronglyMeasurablestatement and proof · cited by 1
- Finset.card_nsmul_monostatement and proof · cited by 1
- Finset.Nontrivial.nsmulstatement and proof · cited by 1
- Finset.Nonempty.card_nsmul_monostatement and proof · cited by 1
- Measurable.simpleFunc_addstatement and proof · cited by 1
- Finset.HasAntidiagonal.antidiagonal_subtype_extstatement and proof · cited by 1