Theorems · Theorem · group theory
AddChar.mulShift_apply
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : CommMonoid M] {ψ : AddChar R M} {r x : R},
(ψ.mulShift r) x = ψ (r * x)- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
- Assumes
- RingCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- CommMonoidstatement and proof · cited by 2,264
- AddCharstatement and proof · cited by 286
- AddChar.mulShiftstatement · cited by 26
Cited by9
Results whose statement or proof uses this declaration.
- AddChar.inv_mulShiftproof · cited by 2
- AddChar.mulShift_mulproof · cited by 2
- AddChar.mulShift_oneproof · cited by 2
- AddChar.mulShift_zeroproof · cited by 2
- AddChar.zmod_char_primitive_of_eq_one_only_at_zeroproof · cited by 2
- AddChar.exists_divisor_of_not_isPrimitiveproof · cited by 1
- AddChar.mulShift_spec'proof · cited by 1
- DirichletCharacter.fourierTransform_eq_gaussSum_mulShiftproof · cited by 1
- AddChar.IsPrimitive.zmod_char_eq_one_iffproof · cited by 1