Theorems · Theorem · ring theory
Unitary.mul_right_inj
∀ {R : Type u_1} [inst : Monoid R] [inst_1 : StarMul R] {x y : R} (U : ↥(unitary R)), ↑U * x = ↑U * y ↔ x = yFor unitary U in a star-monoid R, U * x = U * y if and only if x = y
for all x and y in R.
- Defined in
- Mathlib.Algebra.Star.Unitary
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- unitarystatement and proof · cited by 207
- StarMulstatement and proof · cited by 195
- Unitary.toUnitsproof · cited by 18
- Unitary.val_toUnits_applyproof · cited by 7
- Units.mul_right_injproof · cited by 4
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