Theorems · Theorem · group theory
add_sub_cancel_right
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), a + b - b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 187 results in Mathlib
- Foundations
- Depth 10 from the axioms, rests on 40 definitions · uses no axioms
- 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_cancel_rightproof · cited by 65
Cited by187
Results whose statement or proof uses this declaration.
- add_sub_add_right_eq_subproof · cited by 29
- eq_sub_of_add_eqproof · cited by 21
- closure_ballproof · cited by 20
- sub_add_cancel_rightproof · cited by 17
- intervalIntegral.integral_comp_add_rightproof · cited by 9
- interior_closedBallproof · cited by 8
- Nat.cast_predproof · cited by 8
- sub_eq_of_eq_addproof · cited by 8
- lie_lieproof · cited by 8
- segment_eq_imageproof · cited by 7
- dvd_add_leftproof · cited by 7
- Function.Periodic.intervalIntegral_add_eqproof · cited by 7