Theorems · Theorem · functional analysis

CStarAlgebra.ringInverse_le_ringInverse

∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : A},
  a ≤ b →
    autoParam (IsStrictlyPositive a) CStarAlgebra.ringInverse_le_ringInverse._auto_1 → Ring.inverse b ≤ Ring.inverse a

Defined in: Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order
Cited by: 0 results in Mathlib
Foundations: Depth 325 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CStarAlgebra PartialOrder StarOrderedRing

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

PartialOrderstatement and proof · cited by 6,410
StarOrderedRingstatement and proof · cited by 587
Ring.inversestatement · cited by 160
CStarAlgebrastatement and proof · cited by 123
IsStrictlyPositivestatement and proof · cited by 75
IsStrictlyPositive.of_leproof · cited by 4
CStarAlgebra.antitoneOn_ringInverseproof · cited by 1

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