Theorems · Theorem · order theory

Set.image_const_sub_Icc

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b c : α),
  (fun x => a - x) '' Set.Icc b c = Set.Icc (a - c) (a - b)

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 0 results in Mathlib
Foundations: Depth 30 from the axioms · uses propext, Quot.sound
Assumes: AddCommGroup PartialOrder IsOrderedAddMonoid

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Setstatement and proof · cited by 53,352
AddCommGroupstatement and proof · cited by 12,871
PartialOrderstatement and proof · cited by 6,410
Set.imagestatement and proof · cited by 5,609
Set.preimageproof · cited by 4,946
Set.Iccstatement and proof · cited by 1,702
IsOrderedAddMonoidstatement and proof · cited by 1,659
add_commproof · cited by 1,535
sub_eq_add_negproof · cited by 1,023
neg_negproof · cited by 960
Set.image_congrproof · cited by 533
Set.image_compproof · cited by 142

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