Theorems · Theorem · group theory
sub_add_eq_add_sub
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b c : α), a - b + c = a + c - b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- add_assocproof · cited by 746
- SubtractionCommMonoidstatement and proof · cited by 79
- add_left_commproof · cited by 76
Cited by29
Results whose statement or proof uses this declaration.
- sub_eq_sub_iff_add_eq_addproof · cited by 9
- midpoint_eq_smul_addproof · cited by 6
- groupCohomology.mem_cocycles₁_iffproof · cited by 6
- groupCohomology.mem_cocycles₂_iffproof · cited by 5
- Complex.cos_two_mulproof · cited by 3
- hasSum_ite_sub_hasSumproof · cited by 3
- sub_eq_sub_iff_sub_eq_subproof · cited by 2
- Real.Angle.sin_eq_iff_coe_eq_or_add_eq_piproof · cited by 2
- EuclideanDomain.xgcdAux_Pproof · cited by 1
- QuadraticMap.polar_add_left_iffproof · cited by 1
- Antitone.tendsto_le_alternating_seriesproof · cited by 1