Theorems · Theorem · order theory
IsLeast.minimal_iff
∀ {α : Type u_2} {a x : α} {s : Set α} [inst : PartialOrder α], IsLeast s a → (Minimal (fun x => x ∈ s) x ↔ x = a)- Defined in
- Mathlib.Order.Minimal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrder
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
- PartialOrderstatement and proof · cited by 6,410
- Minimalstatement and proof · cited by 150
- IsLeaststatement and proof · cited by 122
- Minimal.propproof · cited by 23
- Minimal.eq_of_geproof · cited by 7
- IsLeast.minimalproof · cited by 1
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