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Theorems · Theorem · functional analysis

IsStarProjection.one_sub_nonneg

∀ {R : Type u_1} [inst : Ring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R] {p : R},
  IsStarProjection p → 0 ≤ 1 - p
Defined in
Mathlib.Algebra.Order.Star.Basic
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingPartialOrderStarRingStarOrderedRing
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Around this declaration

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

IsStarProjection.le_one · cited by 1IsStarProjection.le_oneRing · cited by 7463RingPartialOrder · cited by 6410PartialOrderStarRing · cited by 1686StarRingStarOrderedRing · cited by 587StarOrderedRingIsStarProjection · cited by 64IsStarProjectionIsStarProjection.nonneg · cited by 6IsStarProjection.nonnegIsStarProjection.one_sub · cited by 2IsStarProjection.one_subIsStarProjection.one_sub_nonn…CITED BYCITES

Cites7

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

Cited by1

Results whose statement or proof uses this declaration.