# mathlibdocumentation

data.equiv.option

# Equivalences for option α#

We define remove_none which acts to provide a e : α ≃ β if given a f : option α ≃ option β.

To construct an f : option α ≃ option β from e : α ≃ β such that f none = none and f (some x) = some (e x), use f = equiv_functor.map_equiv option e.

def equiv.remove_none {α : Type u_1} {β : Type u_2} (e : ) :
α β

Given an equivalence between two option types, eliminate none from that equivalence by mapping e.symm none to e none.

Equations
@[simp]
theorem equiv.remove_none_symm {α : Type u_1} {β : Type u_2} (e : ) :
theorem equiv.remove_none_some {α : Type u_1} {β : Type u_2} (e : ) {x : α} (h : ∃ (x' : β), e (some x) = some x') :
theorem equiv.remove_none_none {α : Type u_1} {β : Type u_2} (e : ) {x : α} (h : e (some x) = none) :
@[simp]
theorem equiv.option_symm_apply_none_iff {α : Type u_1} {β : Type u_2} (e : ) :
theorem equiv.some_remove_none_iff {α : Type u_1} {β : Type u_2} (e : ) {x : α} :
@[simp]
theorem equiv.remove_none_map_equiv {α β : Type u_1} (e : α β) :