Theorems · Theorem · group theory
sub_eq_iff_eq_add
∀ {G : Type u_3} [inst : AddGroup G] {a b c : G}, a - b = c ↔ a = c + b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- sub_eq_add_negproof · cited by 1,023
- add_neg_eq_iff_eq_addproof · cited by 12
Cited by74
Results whose statement or proof uses this declaration.
- Int.cast_addproof · cited by 124
- sub_eq_iff_eq_add'proof · cited by 33
- PowerSeries.IsWeierstrassDivisorAt.isWeierstrassDivisionAt_div_modproof · cited by 10
- sub_eq_sub_iff_add_eq_addproof · cited by 9
- sub_halfproof · cited by 7
- Sbtw.angle₁₂₃_eq_piproof · cited by 6
- Affine.Simplex.point_vsub_centroid_eq_smul_vsubproof · cited by 4
- QuadraticMap.polar_selfproof · cited by 3
- Polynomial.modByMonic_eq_of_dvd_subproof · cited by 3
- Real.Angle.cos_eq_iff_coe_eq_or_eq_negproof · cited by 3
- sub_eq_iff_commproof · cited by 3
- Polynomial.Sequence.span_degreeLTproof · cited by 3