Theorems · Theorem · order theory
Set.IsWF.min_le_min_of_subset
∀ {α : Type u_2} [inst : LinearOrder α] {s t : Set α} {hs : s.IsWF} {hsn : s.Nonempty} {ht : t.IsWF} {htn : t.Nonempty},
s ⊆ t → ht.min htn ≤ hs.min hsn- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptystatement and proof · cited by 2,627
- Set.IsWFstatement and proof · cited by 47
- Set.IsWF.minstatement · cited by 47
- Set.IsWF.min_leproof · cited by 14
- Set.IsWF.le_min_iffproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- HahnSeries.order_mul_of_ne_zeroproof · cited by 3
- HahnSeries.orderTop_mul_of_ne_zeroproof · cited by 2
- HahnSeries.min_le_min_addproof · cited by 2
- Set.IsWF.min_unionproof · cited by 1
- HahnModule.orderTop_vAdd_le_orderTop_smulproof · cited by 1
- HahnSeries.order_lt_order_of_eq_add_singleproof · cited by 1
- HahnSeries.order_mulproof · cited by 1