Theorems · Theorem · group theory
AddChar.map_neg_eq_inv
∀ {A : Type u_1} {M : Type u_2} [inst : AddGroup A] [inst_1 : DivisionMonoid M] (ψ : AddChar A M) (a : A),
ψ (-a) = (ψ a)⁻¹An additive character maps negatives to inverses (when defined)
- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroupDivisionMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- AddCharstatement and proof · cited by 286
- neg_add_cancelproof · cited by 256
- DivisionMonoidstatement and proof · cited by 201
- AddChar.map_zero_eq_oneproof · cited by 17
- eq_inv_of_mul_eq_one_leftproof · cited by 15
Cited by9
Results whose statement or proof uses this declaration.
- Circle.star_addCharproof · cited by 3
- AddChar.map_neg_eq_conjproof · cited by 2
- AddChar.wInner_cWeight_eq_booleproof · cited by 2
- VectorFourier.integral_sesq_fourierIntegral_eq_neg_flipproof · cited by 1
- BoundedContinuousFunction.ext_of_char_eqproof · cited by 1
- AddChar.neg_apply'proof · cited by 1
- AddChar.inv_apply'proof · cited by 1
- AddChar.sub_apply'proof · cited by 0
- AddChar.div_apply'proof · cited by 0