Theorems · Theorem · group theory
inv_mul_cancel_right
∀ {G : Type u_1} [inst : Group G] (a b : G), a * b⁻¹ * b = a- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- inv_mul_cancelproof · cited by 107
Cited by70
Results whose statement or proof uses this declaration.
- Matrix.det_mulproof · cited by 51
- div_mul_cancelproof · cited by 33
- Set.image_mul_rightproof · cited by 24
- zpow_add_oneproof · cited by 18
- mul_inv_eq_iff_eq_mulproof · cited by 13
- eq_mul_inv_iff_mul_eqproof · cited by 11
- inv_le_inv_iffproof · cited by 11
- inv_lt_inv_iffproof · cited by 9
- div_le_iff_le_mulproof · cited by 6
- edist_inv_invproof · cited by 6
- div_lt_iff_lt_mulproof · cited by 5
- lt_div_iff_mul_ltproof · cited by 4