Theorems · Theorem · group theory
one_mul
∀ {M : Type u} [inst : MulOneClass M] (a : M), 1 * a = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2,841 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 18 definitions · uses no axioms
- Assumes
- MulOneClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulOneClassstatement and proof · cited by 1,018
- MulOneClass.one_mulproof · cited by 1
Cited by2,841
Results whose statement or proof uses this declaration.
- pow_oneproof · cited by 894
- nsmul_eq_mulproof · cited by 369
- two_mulproof · cited by 232
- zsmul_eq_mulproof · cited by 120
- Int.cast_mulproof · cited by 113
- inv_mul_cancel_leftproof · cited by 88
- mul_inv_cancel_leftproof · cited by 86
- Finset.prod_mul_distribproof · cited by 68
- neg_one_mulproof · cited by 61
- Polynomial.coeff_X_powproof · cited by 50
- inv_mul_cancel_left₀proof · cited by 47
- mul_one_divproof · cited by 45
Showing the 200 most cited of 2,841.