Theorems · Theorem · number theory
MulChar.inv_mul
∀ {R : Type u_1} [inst : CommMonoid R] {R' : Type u_2} [inst_1 : CommMonoidWithZero R'] (χ : MulChar R R'), χ⁻¹ * χ = 1The product of a character with its inverse is the trivial character.
- Defined in
- Mathlib.NumberTheory.MulChar.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidCommMonoidWithZero
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Unitsproof · cited by 2,804
- CommMonoidstatement and proof · cited by 2,264
- Units.valproof · cited by 1,966
- CommMonoidWithZerostatement and proof · cited by 913
- MulCharstatement and proof · cited by 186
- Units.isUnitproof · cited by 116
- IsUnit.mapproof · cited by 104
- Pi.mul_applyproof · cited by 24
- MulChar.extproof · cited by 16
- MulChar.one_apply_coeproof · cited by 13
- Ring.inverse_mul_cancelproof · cited by 6
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