Theorems · Theorem · ring theory
left_distrib
∀ {R : Type v} [inst : Mul R] [inst_1 : Add R] [LeftDistribClass R] (a b c : R), a * (b + c) = a * b + a * c- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- MulAddLeftDistribClass
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.
- LeftDistribClassstatement and proof · cited by 12
- LeftDistribClass.left_distribproof · cited by 1
Cited by19
Results whose statement or proof uses this declaration.
- mul_addproof · cited by 413
- mul_twoproof · cited by 43
- dvd_addproof · cited by 25
- Polynomial.mahlerMeasure_mulproof · cited by 5
- MultilinearMap.norm_image_sub_le_of_bound'proof · cited by 3
- MeasureTheory.Measure.prod_addproof · cited by 2
- Polynomial.isCoprime_X_sub_C_of_isUnit_subproof · cited by 2
- Pell.xn_modEq_x2n_addproof · cited by 2
- SemiconjBy.add_leftproof · cited by 2
- SemiconjBy.add_rightproof · cited by 2
- MvPolynomial.IsWeightedHomogeneous.sum_weight_X_mul_pderivproof · cited by 1
- MvPolynomial.mul_esymm_eq_sumproof · cited by 1