Theorems · Theorem · order theory

Set.image_inv_Iic

∀ {α : Type u_1} [inst : CommGroup α] [inst_1 : PartialOrder α] [IsOrderedMonoid α] (a : α),
  Inv.inv '' Set.Iic a = Set.Ici a⁻¹

Defined in: Mathlib.Algebra.Order.Group.Pointwise.Interval
Cited by: 0 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Quot.sound
Assumes: CommGroup PartialOrder IsOrderedMonoid

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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
PartialOrderstatement and proof · cited by 6,410
Set.imagestatement · cited by 5,609
Set.Iicstatement · cited by 1,111
Set.Icistatement and proof · cited by 1,070
CommGroupstatement and proof · cited by 990
IsOrderedMonoidstatement and proof · cited by 577
Set.image_inv_eq_invproof · cited by 44
Set.inv_Iicproof · cited by 5

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