Theorems · Theorem · ring theory
sub_mul
∀ {α : Type u} [inst : NonUnitalNonAssocRing α] (a b c : α), (a - b) * c = a * c - b * cAlias of mul_sub_right_distrib.
- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 170 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_right_distribproof · cited by 4
Cited by170
Results whose statement or proof uses this declaration.
- IsIdempotentElem.one_subproof · cited by 20
- Algebra.mul_sub_algebraMap_commutesproof · cited by 8
- sub_one_mulproof · cited by 7
- Real.sin_pi_over_two_pow_succproof · cited by 6
- Complex.hasStrictDerivAt_sinproof · cited by 5
- one_sub_mulproof · cited by 5
- LieModule.traceForm_apply_lie_applyproof · cited by 5
- Asymptotics.isEquivalent_iff_exists_eq_mulproof · cited by 4
- Convexity.dist_convexCombPair_leftproof · cited by 4
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- signedDist_lineMap_lineMapproof · cited by 4
- IsIdempotentElem.one_sub_mul_selfproof · cited by 4