Theorems · Theorem · group theory
add_zero
∀ {M : Type u} [inst : AddZeroClass M] (a : M), a + 0 = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2,707 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 18 definitions · uses no axioms
- Assumes
- AddZeroClass
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.
- AddZeroClassstatement and proof · cited by 1,237
- AddZeroClass.add_zeroproof · cited by 1
Cited by2,711
Results whose statement or proof uses this declaration.
- sub_zeroproof · cited by 938
- Nat.cast_addproof · cited by 586
- Finset.sum_singletonproof · cited by 251
- Complex.ofReal_mulproof · cited by 180
- tsub_zeroproof · cited by 123
- sq_nonnegproof · cited by 106
- Complex.ofReal_addproof · cited by 94
- neg_add_cancel_rightproof · cited by 75
- Submodule.mem_supproof · cited by 73
- le_add_of_nonneg_rightproof · cited by 69
- norm_add_leproof · cited by 68
- add_neg_cancel_rightproof · cited by 65
Showing the 200 most cited of 2,711.