Theorems · Theorem · ring theory
mul_sub
∀ {α : Type u} [inst : NonUnitalNonAssocRing α] (a b c : α), a * (b - c) = a * b - a * cAlias of mul_sub_left_distrib.
- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 201 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 82 definitions · uses no axioms
- Assumes
- NonUnitalNonAssocRing
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.
- NonUnitalNonAssocRingstatement · cited by 354
- mul_sub_left_distribproof · cited by 9
Cited by201
Results whose statement or proof uses this declaration.
- IsIdempotentElem.one_subproof · cited by 20
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- mul_one_subproof · cited by 9
- mul_sub_oneproof · cited by 8
- Algebra.mul_sub_algebraMap_commutesproof · cited by 8
- PowerSeries.IsWeierstrassDivisorAt.eq_of_mul_add_eq_mul_addproof · cited by 7
- AddCircle.norm_eqproof · cited by 6
- UpperHalfPlane.cmp_dist_eq_cmp_dist_coe_centerproof · cited by 5
- LieModule.traceForm_apply_lie_applyproof · cited by 5
- ProbabilityTheory.covariance_smul_leftproof · cited by 4
- Complex.cosh_sub_sinhproof · cited by 4
- Commute.mul_self_sub_mul_self_eqproof · cited by 4
Showing the 200 most cited of 201.