Theorems · Theorem · functional analysis
IsStrictlyPositive.iff_of_unital
∀ {A : Type u_1} [inst : LE A] [inst_1 : Monoid A] [inst_2 : Zero A] {a : A}, IsStrictlyPositive a ↔ 0 ≤ a ∧ IsUnit a- Defined in
- Mathlib.Algebra.Algebra.StrictPositivity
- Cited by
- 7 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 · cited by 75
Cited by7
Results whose statement or proof uses this declaration.
- CStarAlgebra.isStrictlyPositive_TFAEproof · cited by 7
- IsUnit.isStrictlyPositiveproof · cited by 5
- Units.isStrictlyPositive_iffproof · cited by 3
- isStrictlyPositive_oneproof · cited by 1
- CFC.isUnit_sqrt_iff_isStrictlyPositiveproof · cited by 1
- IsStrictlyPositive.of_subsingletonproof · cited by 0
- isStrictlyPositive_ringInverse_iffproof · cited by 0