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Theorems · Theorem · order theory

Set.IsWF.min_of_subset_not_lt_min

∀ {α : Type u_2} [inst : Preorder α] {s t : Set α} {hs : s.IsWF} {hsn : s.Nonempty} {ht : t.IsWF} {htn : t.Nonempty},
  s ⊆ t → ¬hs.min hsn < ht.min htn
Defined in
Mathlib.Order.WellFoundedSet
Cited by
2 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

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

HahnSeries.orderTop_smul_not_lt · cited by 2HahnSeries.orderTop_smul_…HahnSeries.order_smul_not_lt · cited by 1HahnSeries.order_smul_not…Set · cited by 53352SetPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptySet.IsWF · cited by 47Set.IsWFSet.IsWF.min · cited by 47IsWF.minSet.IsWF.min_mem · cited by 20IsWF.min_memSet.IsWF.not_lt_min · cited by 7IsWF.not_lt_minIsWF.min_of_subset_not_lt_minCITED BYCITES

Cites7

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Cited by2

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