Theorems · Theorem · order theory
Set.Icc_subset_Icc_left
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b : α}, a₁ ≤ a₂ → Set.Icc a₂ b ⊆ Set.Icc a₁ b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- le_rflproof · cited by 1,558
- Set.Icc_subset_Iccproof · cited by 27
Cited by6
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_deriv_smul_comp'''proof · cited by 4
- StrictMonoOn.strictConvexOn_of_derivproof · cited by 4
- MonotoneOn.convexOn_of_derivproof · cited by 4
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- EulerSine.tendsto_integral_cos_pow_mul_divproof · cited by 1
- ODE_solution_unique_of_mem_Iccproof · cited by 0