Theorems · Theorem · order theory
Pi.exists_forall_antisymmRel_of_wcovBy
∀ {ι : Type u_3} {α : ι → Type u_4} [inst : (i : ι) → Preorder (α i)] {a b : (i : ι) → α i} [Nonempty ι],
a ⩿ b → ∃ i, ∀ (j : ι), j ≠ i → AntisymmRel (fun x1 x2 => x1 ≤ x2) (a j) (b j)- Defined in
- Mathlib.Order.Cover
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Preorderstatement and proof · cited by 7,952
- CovByproof · cited by 290
- WCovBystatement and proof · cited by 107
- AntisymmRelstatement · cited by 93
- wcovBy_iff_covBy_or_le_and_leproof · cited by 3
- Pi.exists_forall_antisymmRel_of_covByproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Pi.wcovBy_iff_antisymmRelproof · cited by 1
- Pi.exists_forall_eq_of_wcovByproof · cited by 0
- Pi.covBy_iff_antisymmRelproof · cited by 0