Theorems · Theorem · group theory

Set.image_neg_of_apply_neg_eq

∀ {α : Type u_2} {β : Type u_3} [inst : InvolutiveNeg α] {s : Set α} {f g : α → β},
  (∀ x ∈ s, f (-x) = g x) → f '' (-s) = g '' s

Defined in: Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 10 from the axioms · uses propext, Quot.sound
Assumes: InvolutiveNeg

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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 and proof · cited by 5,609
Set.image_congrproof · cited by 533
Set.negstatement · cited by 168
InvolutiveNegstatement and proof · cited by 151
Set.image_imageproof · cited by 140
Set.image_neg_eq_negproof · cited by 52

Cited by1

Results whose statement or proof uses this declaration.

Set.image_neg_of_apply_neg_eq_negproof · cited by 0