Theorems · Theorem · group theory
SemiconjBy.units_inv_symm_left
∀ {M : Type u_1} [inst : Monoid M] {a : Mˣ} {x y : M}, SemiconjBy (↑a) x y → SemiconjBy (↑a⁻¹) y xIf a unit a semiconjugates x to y, then a⁻¹ semiconjugates y to x.
- Defined in
- Mathlib.Algebra.Group.Semiconj.Units
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
- SemiconjBystatement and proof · cited by 99
- Units.mul_inv_cancel_rightproof · cited by 20
- SemiconjBy.eqproof · cited by 18
- Units.inv_mul_cancel_leftproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- IsConj.symmproof · cited by 6
- SemiconjBy.units_inv_symm_left_iffproof · cited by 2
- Commute.units_inv_leftproof · cited by 1