Theorems · Theorem · ring theory
mul_sub_one
∀ {α : Type u} [inst : NonAssocRing α] (a b : α), a * (b - 1) = a * b - a- Defined in
- Mathlib.Algebra.Ring.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- NonAssocRingstatement and proof · cited by 483
- mul_subproof · cited by 201
Cited by8
Results whose statement or proof uses this declaration.
- multipliable_one_add_of_summableproof · cited by 4
- dvd_pow_pow_sub_self_of_dvdproof · cited by 2
- norm_commutator_units_sub_one_leproof · cited by 2
- Submodule.re_inner_starProjection_eq_normSqproof · cited by 1
- Matrix.commutator_diag2_transvectionproof · cited by 1
- UniformContinuousOn.cexpproof · cited by 1
- Matrix.transvection_mem_commutator₁proof · cited by 1
- Real.sqrt_le_self_iffproof · cited by 0