Theorems · Theorem · functional analysis
IsUnit.isStrictlyPositive
∀ {A : Type u_1} [inst : LE A] [inst_1 : Monoid A] [inst_2 : Zero A] {a : A}, IsUnit a → 0 ≤ a → IsStrictlyPositive a- Defined in
- Mathlib.Algebra.Algebra.StrictPositivity
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 1,602
- IsStrictlyPositivestatement · cited by 75
- IsStrictlyPositive.iff_of_unitalproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- CStarAlgebra.isStrictlyPositive_TFAEproof · cited by 7
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
- IsStrictlyPositive.smulproof · cited by 1
- le_iff_norm_sqrt_mul_sqrt_invproof · cited by 1
- IsStrictlyPositive.commute_iffproof · cited by 0