Theorems · Theorem · functional analysis
conjugate_le_conjugate_of_nonneg
∀ {R : Type u_1} [inst : NonUnitalSemiring R] [inst_1 : PartialOrder R] [inst_2 : StarRing R] [StarOrderedRing R]
{a b : R}, a ≤ b → ∀ {c : R}, 0 ≤ c → c * a * c ≤ c * b * c- Defined in
- Mathlib.Algebra.Order.Star.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalSemiringstatement and proof · cited by 339
- IsSelfAdjoint.of_nonnegproof · cited by 43
- IsSelfAdjoint.conjugate_le_conjugateproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- le_iff_norm_sqrt_mul_rpowproof · cited by 1