Theorems · Theorem · group theory
sub_add_cancel
∀ {G : Type u_1} [inst : AddGroup G] (a b : G), a - b + b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 344 results in Mathlib
- Foundations
- Depth 8 from the axioms, rests on 40 definitions · 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_eq_add_negproof · cited by 1,023
- neg_add_cancel_rightproof · cited by 75
Cited by344
Results whose statement or proof uses this declaration.
- sub_add_sub_cancelproof · cited by 56
- Polynomial.Chebyshev.T_add_twoproof · cited by 20
- closure_ballproof · cited by 20
- Real.exp_strictMonoproof · cited by 17
- Polynomial.Chebyshev.U_add_twoproof · cited by 16
- Polynomial.Chebyshev.C_add_twoproof · cited by 13
- Function.Periodic.sub_eqproof · cited by 13
- hasSum_nat_add_iff'proof · cited by 12
- tendsto_sub_nhds_zero_iffproof · cited by 12
- Function.Antiperiodic.sub_eqproof · cited by 12
- Polynomial.Chebyshev.S_add_twoproof · cited by 11
- Matrix.charpoly_monicproof · cited by 9
Showing the 200 most cited of 344.