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set_theory.​schroeder_bernstein

set_theory.​schroeder_bernstein

source
function.​embedding.​antisymm
function.​embedding.​min_injective
function.​embedding.​schroeder_bernstein
function.​embedding.​total
source
theorem function.​embedding.​schroeder_bernstein {α : Type u} {β : Type v} {f : α → β} {g : β → α} :
function.injective f → function.injective g → (∃ (h : α → β), function.bijective h)

source
theorem function.​embedding.​antisymm {α : Type u} {β : Type v} :
(α ↪ β) → (β ↪ α) → nonempty (α ≃ β)

source
theorem function.​embedding.​min_injective {ι : Type u} {β : ι → Type v} :
nonempty ι → (∃ (i : ι), nonempty (Π (j : ι), β i ↪ β j))

source
theorem function.​embedding.​total {α : Type u} {β : Type v} :
nonempty (α ↪ β) ∨ nonempty (β ↪ α)

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