mathlib3 documentation

data.prod.pprod

Extra facts about pprod #

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@[simp]
theorem pprod.mk.eta {α : Sort u_1} {β : Sort u_2} {p : pprod α β} :
p.fst, p.snd = p
@[simp]
theorem pprod.forall {α : Sort u_1} {β : Sort u_2} {p : pprod α β Prop} :
( (x : pprod α β), p x) (a : α) (b : β), p a, b⟩
@[simp]
theorem pprod.exists {α : Sort u_1} {β : Sort u_2} {p : pprod α β Prop} :
( (x : pprod α β), p x) (a : α) (b : β), p a, b⟩
theorem pprod.forall' {α : Sort u_1} {β : Sort u_2} {p : α β Prop} :
( (x : pprod α β), p x.fst x.snd) (a : α) (b : β), p a b
theorem pprod.exists' {α : Sort u_1} {β : Sort u_2} {p : α β Prop} :
( (x : pprod α β), p x.fst x.snd) (a : α) (b : β), p a b
theorem function.injective.pprod_map {α : Sort u_1} {β : Sort u_2} {γ : Sort u_3} {δ : Sort u_4} {f : α β} {g : γ δ} (hf : function.injective f) (hg : function.injective g) :
function.injective (λ (x : pprod α γ), f x.fst, g x.snd⟩)