Theorems · Theorem · group theory
sub_add_sub_comm
∀ {α : Type u_1} [inst : SubtractionCommMonoid α] (a b c d : α), a - b + (c - d) = a + c - (b + d)- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- SubtractionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_commproof · cited by 1,535
- sub_eq_add_negproof · cited by 1,023
- add_assocproof · cited by 746
- neg_add_revproof · cited by 236
- SubtractionCommMonoidstatement and proof · cited by 79
- add_left_commproof · cited by 76
Cited by10
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_strongDualproof · cited by 3
- KaehlerDifferential.submodule_span_range_eq_idealproof · cited by 2
- abs_sub_sup_add_abs_sub_infproof · cited by 2
- intervalIntegral.integral_add_adjacent_intervals_cancelproof · cited by 1
- UniformConvexOn.addproof · cited by 1
- roth_3ap_theoremproof · cited by 1
- ProbabilityTheory.IndepFun.hasGaussianLaw_sub_of_subproof · cited by 1
- Int.fract_add_fract_leproof · cited by 0
- Int.fract_add_leproof · cited by 0
- IsEllipticNet.atomRel_avg_subproof · cited by 0