Theorems · Theorem · group theory
AddChar.mulShift_mul
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : CommMonoid M] (ψ : AddChar R M) (r s : R),
ψ.mulShift r * ψ.mulShift s = ψ.mulShift (r + s)The product of mulShift ψ r and mulShift ψ s is mulShift ψ (r + s).
- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- RingCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- CommMonoidstatement and proof · cited by 2,264
- AddCharstatement and proof · cited by 286
- right_distribproof · cited by 26
- AddChar.mulShiftstatement and proof · cited by 26
- AddChar.map_add_eq_mulproof · cited by 13
- AddChar.extproof · cited by 11
- AddChar.mulShift_applyproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- gaussSum_aux_of_mulShiftproof · cited by 1
- AddChar.to_mulShift_inj_of_isPrimitiveproof · cited by 0