Theorems · Theorem · group theory
sub_add_sub_cancel
∀ {G : Type u_3} [inst : AddGroup G] (a b c : G), a - b + (b - c) = a - c- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- AddGroup
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.
- AddGroupstatement and proof · cited by 4,410
- sub_add_cancelproof · cited by 344
- add_sub_assocproof · cited by 72
Cited by56
Results whose statement or proof uses this declaration.
- sub_sub_sub_cancel_rightproof · cited by 34
- sub_sub_sub_cancel_leftproof · cited by 23
- sub_add_sub_cancel'proof · cited by 18
- HasFDerivAtFilter.compproof · cited by 13
- IsBoundedBilinearMap.continuousproof · cited by 11
- IsBoundedBilinearMap.hasStrictFDerivAtproof · cited by 7
- abs_sub_leproof · cited by 6
- Commute.mul_self_sub_mul_self_eqproof · cited by 4
- groupCohomology.d₀₁_comp_d₁₂proof · cited by 4
- groupHomology.d₂₁_comp_d₁₀proof · cited by 4
- norm_sub_le_norm_sub_add_norm_subproof · cited by 4
- Real.le_mk_of_forall_leproof · cited by 3