Theorems · Theorem · group theory
left_inv_eq_right_inv
∀ {M : Type u_2} [inst : Monoid M] {a b c : M}, b * a = 1 → a * c = 1 → b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Monoid
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.
Cited by19
Results whose statement or proof uses this declaration.
- invOf_eq_right_invproof · cited by 10
- IsUnit.mem_unitary_iff_star_mul_selfproof · cited by 3
- IsGroupLikeElem.of_mul_eq_oneproof · cited by 2
- invOf_eq_left_invproof · cited by 2
- IsUnit.eq_on_invproof · cited by 2
- inv_uniqueproof · cited by 2
- HopfAlgebra.antipode_comp_mul_comp_commproof · cited by 1
- isStablyFiniteRing_iff_injective_of_surjectiveproof · cited by 1
- ZMod.inv_eq_of_mul_eq_oneproof · cited by 1
- StarSubalgebra.coe_isUnitproof · cited by 1
- isUnit_iff_exists_and_existsproof · cited by 1
- CategoryTheory.HopfObj.mul_antipodeproof · cited by 1