Theorems · Theorem · number theory
MulChar.pow_apply_coe
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] (χ : MulChar R R') (n : ℕ)
(a : Rˣ), (χ ^ n) ↑a = χ ↑a ^ nIf a is a unit and n : ℕ, then (χ ^ n) a = (χ a) ^ n.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valstatement and proof · cited by 1,966
- pow_zeroproof · cited by 1,094
- CommMonoidWithZerostatement and proof · cited by 913
- pow_succproof · cited by 374
- MulCharstatement and proof · cited by 186
- MulChar.one_apply_coeproof · cited by 13
- MulChar.mul_applyproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- MulChar.pow_apply'proof · cited by 7
- MulChar.IsQuadratic.pow_charproof · cited by 2
- MulChar.pow_card_eq_oneproof · cited by 2
- MulChar.isQuadratic_iff_sq_eq_oneproof · cited by 1
- MulChar.zpow_apply_coeproof · cited by 0