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Theorems · Theorem · functional analysis

IsStrictlyPositive.add_nonneg

∀ {A : Type u_1} [inst : CStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a b : A},
  IsStrictlyPositive a → 0 ≤ b → IsStrictlyPositive (a + b)
Defined in
Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order
Cited by
1 results in Mathlib
Foundations
Depth 319 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CStarAlgebraPartialOrderStarOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsStrictlyPositive.nonneg_add · cited by 0IsStrictlyPositive.nonneg…PartialOrder · cited by 6410PartialOrderStarOrderedRing · cited by 587StarOrderedRingCStarAlgebra · cited by 123CStarAlgebraIsStrictlyPositive · cited by 75IsStrictlyPositivele_add_iff_nonneg_right · cited by 15le_add_iff_nonneg_rightIsStrictlyPositive.of_le · cited by 4IsStrictlyPositive.of_leIsStrictlyPositive.add_nonnegCITED BYCITES

Cites6

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Cited by1

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