Theorems · Theorem · ring theory
Commute.add_left
∀ {R : Type u} [inst : Distrib R] {a b c : R}, Commute a c → Commute b c → Commute (a + b) c- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- Distrib
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
- Distribstatement and proof · cited by 31
- SemiconjBy.add_leftproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Nat.cast_commuteproof · cited by 24
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- Commute.cfcHomproof · cited by 2
- Commute.cfcₙHomproof · cited by 2
- Commute.add_pow_dvd_pow_of_pow_eq_zero_rightproof · cited by 1
- Commute.span_leftproof · cited by 1
- Polynomial.smeval_commuteproof · cited by 1
- Polynomial.smeval_commute_leftproof · cited by 1
- Matrix.mem_range_scalar_iff_commute_transvectionStructproof · cited by 0