Theorems · Theorem · order theory
eq_min
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, c ≤ a → c ≤ b → (∀ {d : α}, d ≤ a → d ≤ b → d ≤ c) → c = min a b- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- le_antisymmproof · cited by 2,068
- min_le_leftproof · cited by 105
- min_le_rightproof · cited by 88
- le_minproof · cited by 21
Cited by3
Results whose statement or proof uses this declaration.
- min_eq_leftproof · cited by 67
- min_commproof · cited by 23
- min_assocproof · cited by 5