Theorems · Theorem · group theory
add_add_add_comm
∀ {G : Type u_3} [inst : AddCommSemigroup G] (a b c d : G), a + b + (c + d) = a + c + (b + d)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- 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_assocproof · cited by 746
- AddCommSemigroupstatement and proof · cited by 178
- add_left_commproof · cited by 76
Cited by56
Results whose statement or proof uses this declaration.
- Multiset.sum_map_addproof · cited by 6
- StrictConvexOn.add_convexOnproof · cited by 5
- convex_segmentproof · cited by 5
- ConvexOn.addproof · cited by 4
- Metric.infEDist_le_infEDist_add_hausdorffEDistproof · cited by 4
- AddCommGroup.ModEq.add_iff_leftproof · cited by 3
- Matrix.Nonsingular.of_linearIndependent_colproof · cited by 3
- Convex.translate_preimage_rightproof · cited by 3
- Even.addproof · cited by 3
- IsEllipticNet.rel_eqproof · cited by 3
- AddCommGroup.tfae_modEqproof · cited by 3
- ConvexOn.smul'proof · cited by 3