Theorems · Theorem · number theory
MulChar.one_apply_coe
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] (a : Rˣ), 1 ↑a = 1Evaluation of the trivial character
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 17 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Unitsstatement and proof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valstatement · cited by 1,966
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement · cited by 186
- Units.isUnitproof · cited by 116
Cited by13
Results whose statement or proof uses this declaration.
- MulChar.one_applyproof · cited by 10
- MulChar.pow_apply_coeproof · cited by 5
- MulChar.sum_one_eq_card_unitsproof · cited by 2
- MulChar.pow_card_eq_oneproof · cited by 2
- MulChar.ringHomComp_oneproof · cited by 2
- MulChar.isQuadratic_iff_sq_eq_oneproof · cited by 1
- MulChar.IsQuadratic.gaussSum_frobproof · cited by 1
- MulChar.apply_mem_rootsOfUnity_orderOfproof · cited by 1
- MulChar.one_mulproof · cited by 0
- MulChar.inv_mulproof · cited by 0
- MulChar.eq_one_iffproof · cited by 0
- MulChar.val_neg_one_eq_one_of_odd_orderproof · cited by 0