Theorems · Theorem · group theory
add_left_comm
∀ {G : Type u_3} [inst : AddCommSemigroup G] (a b c : G), a + (b + c) = b + (a + c)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddCommSemigroup
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.
- add_commproof · cited by 1,535
- add_assocproof · cited by 746
- AddCommSemigroupstatement and proof · cited by 178
Cited by76
Results whose statement or proof uses this declaration.
- add_add_add_commproof · cited by 56
- sub_addproof · cited by 51
- Polynomial.derivative_mulproof · cited by 35
- sub_add_eq_add_subproof · cited by 29
- add_sub_add_commproof · cited by 28
- sub_sub_cancel_leftproof · cited by 28
- sub_right_commproof · cited by 15
- mul_le_mul_of_nonpos_rightproof · cited by 13
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- mul_le_mul_of_nonpos_leftproof · cited by 11
- add_sub_right_commproof · cited by 10
- sub_add_sub_commproof · cited by 10