Theorems · Theorem · functional analysis

CFC.log_le_log

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

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Order
Cited by: 0 results in Mathlib
Foundations: Depth 333 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CStarAlgebra PartialOrder StarOrderedRing

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PartialOrderstatement and proof · cited by 6,410
Complexstatement · cited by 5,565
StarOrderedRingstatement and proof · cited by 587
CStarAlgebrastatement and proof · cited by 123
IsStarNormalstatement · cited by 117
IsStrictlyPositivestatement and proof · cited by 75
CFC.logstatement · cited by 17
IsStrictlyPositive.of_leproof · cited by 4
CFC.log_monotoneOnproof · cited by 1

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