Theorems · Theorem · functional analysis
IsStrictlyPositive.isUnit
∀ {A : Type u_1} [inst : LE A] [inst_1 : Monoid A] [inst_2 : Zero A] {a : A}, IsStrictlyPositive a → IsUnit a- Defined in
- Mathlib.Algebra.Algebra.StrictPositivity
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- IsUnitstatement · cited by 1,602
- IsStrictlyPositivestatement and proof · cited by 75
Cited by12
Results whose statement or proof uses this declaration.
- CStarAlgebra.isStrictlyPositive_TFAEproof · cited by 7
- CFC.rpow_rpowproof · cited by 6
- CFC.inverse_eq_rpow_neg_oneproof · cited by 4
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
- CFC.conjugate_rpow_neg_one_halfproof · cited by 1
- IsStrictlyPositive.smulproof · cited by 1
- CFC.rpow_neg_mul_rpowproof · cited by 1
- le_iff_norm_sqrt_mul_rpowproof · cited by 1
- CStarAlgebra.rpow_neg_one_le_rpow_neg_oneproof · cited by 1
- CFC.continuousOn_rpowproof · cited by 0
- CFC.rpow_mul_rpow_negproof · cited by 0
- IsStrictlyPositive.commute_iffproof · cited by 0