Theorems · Theorem · order theory
Set.Icc_inter_Icc
∀ {α : Type u_1} [inst : Lattice α] {a₁ a₂ b₁ b₂ : α}, Set.Icc a₁ b₁ ∩ Set.Icc a₂ b₂ = Set.Icc (a₁ ⊔ a₂) (b₁ ⊓ b₂)- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderproof · cited by 7,952
- Set.Iccstatement · cited by 1,702
- Set.Iicproof · cited by 1,111
- Set.Iciproof · cited by 1,070
- Latticestatement and proof · cited by 916
- SemilatticeSupproof · cited by 785
- SemilatticeInfproof · cited by 634
- Set.Ici_inter_Iicproof · cited by 12
- Set.Iic_inter_Iicproof · cited by 9
- Set.Ici_inter_Iciproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.BrownianReal.posSemidef_covMatrixproof · cited by 2
- Interval.coe_infproof · cited by 1
- isPiSystem_Iccproof · cited by 1
- HasConstantSpeedOnWith.Icc_Iccproof · cited by 1
- isPiSystem_Icc_memproof · cited by 0