Theorems · Theorem · group theory
one_nsmul
∀ {M : Type u_2} [inst : AddMonoid M] (a : M), 1 • a = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- zero_addproof · cited by 2,366
- zero_nsmulproof · cited by 137
- succ_nsmulproof · cited by 65
Cited by64
Results whose statement or proof uses this declaration.
- two_nsmulproof · cited by 67
- one_zsmulproof · cited by 59
- add_one_zsmulproof · cited by 19
- ArchimedeanClass.mk_negproof · cited by 15
- neg_one_zsmulproof · cited by 14
- Derivation.leibniz_powproof · cited by 10
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonposproof · cited by 6
- ArchimedeanClass.lt_of_mk_lt_mk_of_nonnegproof · cited by 5
- Finset.sum_update_of_memproof · cited by 5
- multiplesHomproof · cited by 5
- Filter.Tendsto.nsmul_atTopproof · cited by 4
- le_self_nsmulproof · cited by 3