Theorems · Theorem · ring theory
Commute.sub_right
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {a b c : R}, Commute a b → Commute a c → Commute a (b - c)- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- NonUnitalNonAssocRing
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.
- Commutestatement · cited by 639
- NonUnitalNonAssocRingstatement and proof · cited by 354
- SemiconjBy.sub_rightproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Module.End.apply_eq_of_mem_of_comm_of_isFinitelySemisimple_of_isNilproof · cited by 2
- Submodule.inf_iSup_genEigenspaceproof · cited by 1
- isIdempotentElem_one_sub_one_sub_pow_powproof · cited by 1
- LinearMap.trace_comp_eq_mul_of_commute_of_isNilpotentproof · cited by 1
- Module.End.genEigenspace_inf_le_addproof · cited by 1
- Commute.pow_dvd_sub_pow_of_pow_eq_zero_rightproof · cited by 1