Theorems · Theorem · order theory
Set.eq_of_mem_uIcc_of_mem_uIcc
∀ {α : Type u_1} [inst : DistribLattice α] {a b c : α}, a ∈ Set.uIcc b c → b ∈ Set.uIcc a c → a = b- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- DistribLattice
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
- Set.uIccstatement and proof · cited by 393
- DistribLatticestatement and proof · cited by 150
- inf_congr_rightproof · cited by 5
- sup_congr_rightproof · cited by 4
- eq_of_inf_eq_sup_eqproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Set.eq_of_mem_uIcc_of_mem_uIcc'proof · cited by 1
- Set.uIcc_injective_rightproof · cited by 1
- Finset.eq_of_mem_uIcc_of_mem_uIccproof · cited by 1