Theorems · Theorem · functional analysis
star_le_star_iff
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{x y : R}, star x ≤ star y ↔ x ≤ y- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- Set.rangeproof · cited by 4,705
- StarRingstatement and proof · cited by 1,686
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalSemiringstatement and proof · cited by 339
- AddSubmonoid.closureproof · cited by 224
- star_starproof · cited by 135
- StarMul.star_mulproof · cited by 72
- StarAddMonoid.star_addproof · cited by 29
- starAddEquivproof · cited by 25
Cited by6
Results whose statement or proof uses this declaration.
- star_lt_star_iffproof · cited by 5
- star_nonneg_iffproof · cited by 1
- one_le_star_iffproof · cited by 0
- star_nonpos_iffproof · cited by 0
- star_le_iffproof · cited by 0
- star_le_one_iffproof · cited by 0