Theorems · Theorem · order theory
Set.uIoc_of_le
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, a ≤ b → Set.uIoc a b = Set.Ioc a b- Cited by
- 38 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- LinearOrder
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.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iocstatement and proof · cited by 971
- inf_of_le_leftproof · cited by 186
- Set.uIocstatement · cited by 182
- sup_of_le_rightproof · cited by 143
Cited by38
Results whose statement or proof uses this declaration.
- intervalIntegrable_iff_integrableOn_Ioc_of_leproof · cited by 21
- intervalIntegral.intervalIntegral_eq_integral_uIocproof · cited by 17
- intervalIntegral.intervalIntegrable_cpow'proof · cited by 7
- intervalIntegral.intervalIntegrable_rpow'proof · cited by 6
- intervalIntegral.norm_integral_le_integral_normproof · cited by 5
- intervalIntegral.integral_deriv_of_contDiffOn_Iccproof · cited by 4
- MeasureTheory.lintegral_comp_eq_lintegral_meas_le_mulproof · cited by 3
- ValueDistribution.Cartan.integrableOn_cartanKernelproof · cited by 3
- interval_average_eqproof · cited by 3
- Chebyshev.integral_theta_div_log_sq_isBigOproof · cited by 2
- exists_eq_interval_average_of_nullSingletonClassproof · cited by 2
- MeasureTheory.intervalIntegral_integral_swapproof · cited by 2