Theorems · Theorem · order theory
Set.Ico_subset_Ico_right
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b : α}, a₂ ≤ a₁ → Set.Ico b a₂ ⊆ Set.Ico b a₁- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 8 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
- le_rflproof · cited by 1,558
- Set.Icostatement · cited by 799
- Set.Ico_subset_Icoproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- nhdsGE_basis_of_exists_gtproof · cited by 6
- intervalIntegral.sum_integral_adjacent_intervals_Icoproof · cited by 4
- IntervalIntegrable.trans_iterate_Icoproof · cited by 3
- TFAE_mem_nhdsGEproof · cited by 3
- IsClosed.Icc_subset_of_forall_exists_gtproof · cited by 2
- exists_Ico_subset_of_mem_nhds'proof · cited by 1