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Theorems · Theorem · order theory

Set.IsWF.le_min_iff

∀ {α : Type u_2} [inst : LinearOrder α] {s : Set α} {a : α} (hs : s.IsWF) (hn : s.Nonempty),
  a ≤ hs.min hn ↔ ∀ b ∈ s, a ≤ b
Defined in
Mathlib.Order.WellFoundedSet
Cited by
5 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
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Around this declaration

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

Set.IsWF.min_le_min_of_subset · cited by 7IsWF.min_le_min_of_subsetSet.IsWF.min_add · cited by 3IsWF.min_addSet.IsWF.min_vadd · cited by 1IsWF.min_vaddSet.IsWF.min_smul · cited by 0IsWF.min_smulSet.IsWF.min_mul · cited by 0IsWF.min_mulSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.Nonemptyle_trans · cited by 985le_transSet.IsWF · cited by 47Set.IsWFSet.IsWF.min · cited by 47IsWF.minSet.IsWF.min_mem · cited by 20IsWF.min_memSet.IsWF.min_le · cited by 14IsWF.min_leIsWF.le_min_iffCITED BYCITES

Cites8

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

Cited by5

Results whose statement or proof uses this declaration.