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Theorems · Theorem · group theory

Units.embedProduct_apply

∀ (α : Type u_6) [inst : Monoid α] (x : αˣ), (Units.embedProduct α) x = (↑x, MulOpposite.op ↑x⁻¹)
Defined in
Mathlib.Algebra.Group.Prod
Cited by
3 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Quot.sound
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Units.continuous_iff · cited by 3Units.continuous_iffIsOpenUnits.of_isAdic · cited by 0IsOpenUnits.of_isAdicMatrix.GeneralLinearGroup.continuous_upperRightHom · cited by 0GeneralLinearGroup.contin…DFunLike.coe · cited by 62936DFunLike.coeMonoid · cited by 3887MonoidMonoidHom · cited by 3629MonoidHomUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valMulOpposite · cited by 1135MulOppositeMulOpposite.op · cited by 520MulOpposite.opUnits.embedProduct · cited by 12Units.embedProductUnits.embedProduct_applyCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.