Theorems · Theorem · order theory
one_half_pos
∀ {α : Type u_2} [inst : Semifield α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α], 0 < 1 / 2- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 31 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.
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
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_lt_oneproof · cited by 598
- Semifieldstatement and proof · cited by 439
- PosMulReflectLTstatement and proof · cited by 278
- half_posproof · cited by 83
Cited by31
Results whose statement or proof uses this declaration.
- Real.Gamma_one_half_eqproof · cited by 6
- Real.GammaIntegral_convergentproof · cited by 5
- hasSum_geometric_two'proof · cited by 4
- Asymptotics.IsLittleO.right_isBigO_addproof · cited by 3
- not_summable_one_div_on_primesproof · cited by 2
- Real.Gamma_integrand_isLittleOproof · cited by 2
- Complex.hasDerivAt_Gamma_one_halfproof · cited by 2
- Real.Gamma_three_div_two_lt_oneproof · cited by 2
- Complex.summable_log_one_add_of_summableproof · cited by 2
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- Real.hasDerivAt_Gamma_one_halfproof · cited by 1
- Matrix.frobenius_nnnorm_mulproof · cited by 1