Theorems · Theorem · ring theory
mul_sub_left_distrib
∀ {α : Type u} [inst : NonUnitalNonAssocRing α] (a b c : α), a * (b - c) = a * b - a * c- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses no axioms
- Assumes
- NonUnitalNonAssocRing
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.
- sub_eq_add_negproof · cited by 1,023
- mul_addproof · cited by 413
- NonUnitalNonAssocRingstatement and proof · cited by 354
- neg_mul_eq_mul_negproof · cited by 15
Cited by9
Results whose statement or proof uses this declaration.
- mul_subproof · cited by 201
- hasFDerivAt_exp_smul_const_of_mem_ballproof · cited by 3
- inner_sum_smul_sum_smul_of_sum_eq_zeroproof · cited by 1
- Valuation.inversion_estimateproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1
- Pell.xn_modEq_x2n_sub_lemproof · cited by 1
- dvd_mul_sub_mulproof · cited by 1
- MvPolynomial.psum_eq_mul_esymm_sub_sumproof · cited by 0