Theorems · Theorem · group theory
AddSemiconjBy.addUnits_neg_right
∀ {M : Type u_1} [inst : AddMonoid M] {a : M} {x y : AddUnits M}, AddSemiconjBy a ↑x ↑y → AddSemiconjBy a ↑(-x) ↑(-y)If a semiconjugates an additive unit x to an additive unit y, then it
semiconjugates -x to -y.
- Defined in
- Mathlib.Algebra.Group.Semiconj.Units
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- AddMonoid
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.
- AddMonoidstatement and proof · cited by 2,864
- add_assocproof · cited by 746
- AddUnitsstatement and proof · cited by 325
- AddUnits.valstatement and proof · cited by 248
- AddSemiconjBystatement and proof · cited by 56
- AddSemiconjBy.eqproof · cited by 10
- AddUnits.add_neg_cancel_rightproof · cited by 8
- AddUnits.neg_add_cancel_leftproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- AddSemiconjBy.addUnits_zsmul_rightproof · cited by 1
- AddCommute.addUnits_neg_rightproof · cited by 1
- AddSemiconjBy.addUnits_neg_right_iffproof · cited by 1