mathlib documentation

data.ulift

Extra lemmas about ulift and plift #

In this file we provide subsingleton, unique, decidable_eq, and is_empty instances for ulift α and plift α. We also prove ulift.forall, ulift.exists, plift.forall, and plift.exists.

source
@[instance]
def plift.subsingleton {α : Sort u} [subsingleton α] :
subsingleton (plift α)
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@[instance]
def plift.unique {α : Sort u} [unique α] :
unique (plift α)
Equations
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@[instance]
def plift.decidable_eq {α : Sort u} [decidable_eq α] :
decidable_eq (plift α)
Equations
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@[instance]
def plift.is_empty {α : Sort u} [is_empty α] :
is_empty (plift α)
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@[simp]
theorem plift.forall {α : Sort u} {p : plift α → Prop} :
(∀ (x : plift α), p x) ↔ ∀ (x : α), p {down := x}
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@[simp]
theorem plift.exists {α : Sort u} {p : plift α → Prop} :
(∃ (x : plift α), p x) ↔ ∃ (x : α), p {down := x}
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@[instance]
def ulift.subsingleton {α : Type u} [subsingleton α] :
subsingleton (ulift α)
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@[instance]
def ulift.unique {α : Type u} [unique α] :
unique (ulift α)
Equations
source
@[instance]
def ulift.decidable_eq {α : Type u} [decidable_eq α] :
decidable_eq (ulift α)
Equations
source
@[instance]
def ulift.is_empty {α : Type u} [is_empty α] :
is_empty (ulift α)
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@[simp]
theorem ulift.forall {α : Type u} {p : ulift α → Prop} :
(∀ (x : ulift α), p x) ↔ ∀ (x : α), p {down := x}
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@[simp]
theorem ulift.exists {α : Type u} {p : ulift α → Prop} :
(∃ (x : ulift α), p x) ↔ ∃ (x : α), p {down := x}