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Theorems · Theorem · order theory

Set.IsWF.min_eq_of_le

∀ {α : Type u_2} [inst : PartialOrder α] {s : Set α} {a : α} (hs : s.IsWF) (ha : a ∈ s), (∀ b ∈ s, a ≤ b) → hs.min ⋯ = a
Defined in
Mathlib.Order.WellFoundedSet
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrder
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Around this declaration

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

HahnSeries.orderTop_eq_of_le · cited by 3HahnSeries.orderTop_eq_of…Set · cited by 53352SetPartialOrder · cited by 6410PartialOrderSet.IsWF · cited by 47Set.IsWFSet.IsWF.min · cited by 47IsWF.mineq_of_le_of_not_lt · cited by 28eq_of_le_of_not_ltSet.IsWF.min_mem · cited by 20IsWF.min_memSet.nonempty_of_mem · cited by 19Set.nonempty_of_memSet.IsWF.not_lt_min · cited by 7IsWF.not_lt_minIsWF.min_eq_of_leCITED BYCITES

Cites8

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Cited by1

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