Theorems · Theorem · order theory

Set.iUnion_mul_left_image

∀ {α : Type u_2} [inst : Mul α] {s t : Set α}, ⋃ a ∈ s, (fun x => a * x) '' t = s * t

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Lattice
Cited by: 1 results in Mathlib
Foundations: Depth 11 from the axioms · uses propext, Quot.sound
Assumes: Mul

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Cites5

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

Setstatement and proof · cited by 53,352
Set.imagestatement · cited by 5,609
Set.iUnionstatement · cited by 2,483
Set.mulstatement · cited by 297
Set.iUnion_image_leftproof · cited by 15

Cited by1

Results whose statement or proof uses this declaration.

Subgroup.set_mul_normalizer_commproof · cited by 2