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Theorems · Theorem · order theory

lt_or_le_of_directed

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : PredOrder α] [IsPredArchimedean α] {r v₁ v₂ : α},
  v₂ ≤ r → v₁ ≤ r → v₂ < v₁ ∨ v₁ ≤ v₂
Defined in
Mathlib.Order.SuccPred.Archimedean
Cited by
1 results in Mathlib
Foundations
Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderPredOrderIsPredArchimedean
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RootedTree.mem_subtrees_disjoint_iff · cited by 1RootedTree.mem_subtrees_d…PartialOrder · cited by 6410PartialOrderPredOrder · cited by 334PredOrderlt_of_le_of_ne' · cited by 149lt_of_le_of_ne'IsPredArchimedean · cited by 66IsPredArchimedeanne_of_not_ge · cited by 3ne_of_not_gele_total_of_directed · cited by 2le_total_of_directedlt_or_le_of_directedCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.