Theorems · Theorem · order theory
half_le_self
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] {a : α} [IsStrictOrderedRing α],
0 ≤ a → a / 2 ≤ aAlias of the reverse direction of half_le_self_iff.
- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- half_le_self_iffproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Real.lt_sin_mulproof · cited by 1
- IsPicardLindelof.of_contDiffAt_oneproof · cited by 1
- Real.le_sin_mulproof · cited by 1
- Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_leproof · cited by 1
- NNReal.half_le_selfproof · cited by 0