Theorems · Theorem · order theory

Set.preimage_sub_const_Iio

∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] (a b : α),
  (fun x => x - a) ⁻¹' Set.Iio b = Set.Iio (b + a)

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 0 results in Mathlib
Foundations: Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommGroup PartialOrder IsOrderedAddMonoid

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
AddCommGroupstatement and proof · cited by 12,871
PartialOrderstatement and proof · cited by 6,410
Set.preimagestatement and proof · cited by 4,946
IsOrderedAddMonoidstatement and proof · cited by 1,659
Set.Iiostatement and proof · cited by 1,166
sub_eq_add_negproof · cited by 1,023
neg_negproof · cited by 960
Set.preimage_add_const_Iioproof · cited by 9

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