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feat(set_theory/cardinal): missing lemma (#7880)
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Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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semorrison and semorrison committed Jun 11, 2021
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4 changes: 4 additions & 0 deletions src/set_theory/cardinal.lean
Expand Up @@ -1031,6 +1031,10 @@ lift_mk_le.{v u 0}.mpr ⟨embedding.of_surjective _ surjective_onto_image⟩
theorem mk_range_le {α β : Type u} {f : α → β} : mk (range f) ≤ mk α :=
mk_le_of_surjective surjective_onto_range

theorem mk_range_le_lift {α : Type u} {β : Type v} {f : α → β} :
lift.{v u} (mk (range f)) ≤ lift.{u v} (mk α) :=
lift_mk_le.{v u 0}.mpr ⟨embedding.of_surjective _ surjective_onto_range⟩

lemma mk_range_eq (f : α → β) (h : injective f) : mk (range f) = mk α :=
quotient.sound ⟨(equiv.of_injective f h).symm⟩

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