Theorems · Theorem · functional analysis
star_lt_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
- 5 results in Mathlib
- Foundations
- Depth 66 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
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- NonUnitalSemiringstatement and proof · cited by 339
- star_le_star_iffproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- star_neg_iffproof · cited by 0
- one_lt_star_iffproof · cited by 0
- star_lt_iffproof · cited by 0
- star_lt_one_iffproof · cited by 0
- star_pos_iffproof · cited by 0