Theorems · Theorem · group theory
add_comm
∀ {G : Type u_1} [inst : AddCommMagma G] (a b : G), a + b = b + a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 1,535 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 9 definitions · uses no axioms
- Assumes
- AddCommMagma
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.
- AddCommMagmastatement and proof · cited by 32
- AddCommMagma.add_commproof · cited by 1
Cited by1,536
Results whose statement or proof uses this declaration.
- Finset.sum_range_succproof · cited by 121
- tsub_add_cancel_of_leproof · cited by 112
- sq_nonnegproof · cited by 106
- add_right_commproof · cited by 85
- add_left_commproof · cited by 76
- Submodule.mem_supproof · cited by 73
- neg_addproof · cited by 69
- sub_subproof · cited by 54
- sub_addproof · cited by 51
- sub_eq_neg_addproof · cited by 51
- add_topproof · cited by 49
- sub_le_iff_le_add'proof · cited by 41
Showing the 200 most cited of 1,536.