Theorems · Theorem · functional analysis
IsStrictlyPositive.nonneg
∀ {A : Type u_1} [inst : LE A] [inst_1 : Monoid A] [inst_2 : Zero A] {a : A}, IsStrictlyPositive a → 0 ≤ a- Defined in
- Mathlib.Algebra.Algebra.StrictPositivity
- Cited by
- 18 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.
Cites2
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
- IsStrictlyPositivestatement and proof · cited by 75
Cited by18
Results whose statement or proof uses this declaration.
- CFC.rpow_rpowproof · cited by 6
- IsStrictlyPositive.of_leproof · cited by 4
- CFC.inverse_eq_rpow_neg_oneproof · cited by 4
- Units.isStrictlyPositive_iffproof · cited by 3
- CStarAlgebra.isUnit_of_leproof · cited by 3
- Matrix.isStrictlyPositive_iff_posDefproof · cited by 2
- IsStrictlyPositive.isSelfAdjointproof · cited by 2
- CFC.conjugate_rpow_neg_one_halfproof · cited by 1
- IsStrictlyPositive.smulproof · cited by 1
- CStarAlgebra.convexOn_ringInverseproof · cited by 1
- CFC.rpow_neg_mul_rpowproof · cited by 1
- CFC.rpow_rpow_invproof · cited by 1