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surjectivity of SB function does not require injectivity of f #215

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Jul 16, 2024
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surjectivity of SB function does not require injectivity of f #215

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4 changes: 2 additions & 2 deletions MIL/C04_Sets_and_Functions/S03_The_Schroeder_Bernstein_Theorem.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -312,7 +312,7 @@ In both cases, calling the simplifier with ``simp [sbAux]``
applies the corresponding defining equation of ``sbAux``.
BOTH: -/
-- QUOTE:
theorem sb_surjective (hf : Injective f) (hg : Injective g) : Surjective (sbFun f g) := by
theorem sb_surjective (hg : Injective g) : Surjective (sbFun f g) := by
set A := sbSet f g with A_def
set h := sbFun f g with h_def
intro y
Expand Down Expand Up @@ -348,7 +348,7 @@ EXAMPLES: -/
-- QUOTE:
theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Injective f) (hg : Injective g) :
∃ h : α → β, Bijective h :=
⟨sbFun f g, sb_injective f g hf, sb_surjective f g hf hg⟩
⟨sbFun f g, sb_injective f g hf, sb_surjective f g hg⟩
-- QUOTE.

-- Auxiliary information
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