Theorems · Theorem · order theory
List.minimum_cons
∀ {α : Type u_1} [inst : LinearOrder α] (a : α) (l : List α), (a :: l).minimum = min (↑a) l.minimum- Defined in
- Mathlib.Data.List.MinMax
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- WithTopstatement and proof · cited by 3,754
- WithTop.somestatement and proof · cited by 1,128
- le_topproof · cited by 411
- inf_of_le_leftproof · cited by 186
- List.reverseRecOnproof · cited by 29
- List.minimumstatement and proof · cited by 24
- min_assocproof · cited by 5
- List.minimum_concatproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- List.minimum_ne_top_of_length_posproof · cited by 2
- List.le_minimum_of_forall_leproof · cited by 1
- List.foldr_min_of_ne_nilproof · cited by 0
- List.minimum_le_coe_iffproof · cited by 0
- List.minimum_ne_top_of_ne_nilproof · cited by 0
- List.trop_minimumproof · cited by 0
- List.minimum_appendproof · cited by 0