Theorems · Theorem · order theory
Antitone.map_min
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β} {a b : α},
Antitone f → f (min a b) = max (f a) (f b)- Defined in
- Mathlib.Order.MinMax
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrderLinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- Antitonestatement and proof · cited by 563
- le_totalproof · cited by 294
- sup_of_le_leftproof · cited by 218
- inf_of_le_leftproof · cited by 186
- sup_of_le_rightproof · cited by 143
- inf_of_le_rightproof · cited by 128
Cited by5
Results whose statement or proof uses this declaration.
- Fin.preimage_rev_uIccproof · cited by 2
- max_div_div_right_of_nonposproof · cited by 1
- smul_min_of_nonposproof · cited by 0
- Set.monotone_or_antitone_iff_uIccproof · cited by 0
- Fin.preimage_rev_uIooproof · cited by 0