Theorems · Theorem · group theory
add_neg_cancel
∀ {G : Type u_1} [inst : AddGroup G] (a : G), a + -a = 0- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 213 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 34 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
- neg_add_cancelproof · cited by 256
Cited by218
Results whose statement or proof uses this declaration.
- sub_selfproof · cited by 996
- add_neg_cancel_leftproof · cited by 76
- add_neg_cancel_rightproof · cited by 65
- injective_iff_map_eq_zeroproof · cited by 62
- neg_le_neg_iffproof · cited by 57
- neg_lt_neg_iffproof · cited by 39
- vadd_neg_vaddproof · cited by 31
- Left.neg_pos_iffproof · cited by 22
- Complex.exp_ne_zeroproof · cited by 19
- CategoryTheory.shiftEquivproof · cited by 17
- Left.neg_neg_iffproof · cited by 16
- Complex.exp_negproof · cited by 15
Showing the 200 most cited of 218.