Theorems · Theorem · group theory
neg_add_cancel
∀ {G : Type u_1} [inst : AddGroup G] (a : G), -a + a = 0- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 256 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 31 definitions · uses no axioms
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- AddGroup.neg_add_cancelproof · cited by 1
Cited by260
Results whose statement or proof uses this declaration.
- map_negproof · cited by 378
- neg_smulproof · cited by 306
- add_neg_cancelproof · cited by 213
- smul_negproof · cited by 181
- abs_nonnegproof · cited by 168
- neg_add_cancel_leftproof · cited by 84
- neg_add_cancel_rightproof · cited by 75
- add_eq_zero_iff_eq_negproof · cited by 49
- neg_vadd_vaddproof · cited by 34
- vsub_vadd_eq_vsub_subproof · cited by 32
- add_one_zsmulproof · cited by 19
- affineIndependent_iff_linearIndependent_vsubproof · cited by 11
Showing the 200 most cited of 260.