Theorems · Theorem · group theory
add_right_cancel_iff
∀ {G : Type u_1} [inst : Add G] [IsRightCancelAdd G] {a b c : G}, b + a = c + a ↔ b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- AddIsRightCancelAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsRightCancelAddstatement and proof · cited by 69
- add_right_cancelproof · cited by 23
Cited by19
Results whose statement or proof uses this declaration.
- add_eq_rightproof · cited by 17
- norm_add_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zeroproof · cited by 5
- norm_add_sq_eq_norm_sq_add_norm_sq_of_inner_eq_zeroproof · cited by 5
- norm_sub_sq_eq_norm_sq_add_norm_sq_iff_real_inner_eq_zeroproof · cited by 3
- AddRightCancelMonoid.nsmul_eq_nsmul_iff_modEqproof · cited by 3
- PowerSeries.coeff_X_pow_mulproof · cited by 3
- AddRightCancelMonoid.eq_zero_of_add_rightproof · cited by 2
- PowerSeries.coeff_mul_X_powproof · cited by 2
- Nat.add_mod_add_iteproof · cited by 2
- MvPolynomial.IsWeightedHomogeneous.pderivproof · cited by 1
- AddRightCancelMonoid.finite_multiplesproof · cited by 1