Theorems · Theorem · order theory
wcovBy_iff_covBy_or_le_and_le
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a ⩿ b ↔ a ⋖ b ∨ a ≤ b ∧ b ≤ a- Defined in
- Mathlib.Order.Cover
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- CovBystatement and proof · cited by 290
- WCovBystatement and proof · cited by 107
- CovBy.wcovByproof · cited by 15
- WCovBy.leproof · cited by 15
- WCovBy.covBy_of_not_leproof · cited by 2
- LE.le.wcovBy_of_leproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Pi.exists_forall_antisymmRel_of_wcovByproof · cited by 3
- WCovBy.covBy_or_le_and_leproof · cited by 2
- wcovBy_iff_covBy_or_eqproof · cited by 2