Theorems · Theorem · group theory
add_sub_cancel
∀ {G : Type u_3} [inst : AddCommGroup G] (a b : G), a + (b - a) = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 195 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 69 definitions · uses propext
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- add_sub_cancel_leftproof · cited by 198
- add_sub_assocproof · cited by 72
Cited by195
Results whose statement or proof uses this declaration.
- Ideal.comap_map_of_surjectiveproof · cited by 30
- Submodule.isCompl_orthogonalproof · cited by 24
- Submodule.comap_map_eqproof · cited by 23
- add_add_sub_cancelproof · cited by 12
- Submodule.fg_of_fg_map_of_fg_inf_kerproof · cited by 7
- Real.Icc_eq_closedBallproof · cited by 6
- ContinuousLinearMap.isOpenMapproof · cited by 6
- Submodule.inner_orthogonalProjectionOnto_eq_of_mem_rightproof · cited by 5
- LinearMap.isCompl_of_projproof · cited by 5
- HasFiniteFPowerSeriesOnBall.cpolynomialAt_of_memproof · cited by 5
- Algebra.FormallyUnramified.of_isSeparableproof · cited by 5
- Int.floor_add_fractproof · cited by 4