Theorems · Theorem · order theory
le_total_of_directed
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] [IsPredArchimedean α] {r v₁ v₂ : α},
v₁ ≤ r → v₂ ≤ r → v₂ ≤ v₁ ∨ v₁ ≤ v₂- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Nat.iterateproof · cited by 740
- PredOrderstatement and proof · cited by 334
- Order.predproof · cited by 273
- IsPredArchimedeanstatement and proof · cited by 66
- Function.iterate_addproof · cited by 11
- LE.le.exists_pred_iterateproof · cited by 6
- Order.pred_iterate_leproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- lt_or_le_of_directedproof · cited by 1
- RootedTree.mem_subtrees_disjoint_iffproof · cited by 1