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lines changed Original file line number Diff line number Diff line change @@ -260,7 +260,7 @@ lemma inj_on_iff_injective : inj_on f s ↔ injective (restrict f s) :=
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⟨λ H a b h, subtype.eq $ H a.2 b.2 h,
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λ H a as b bs h, congr_arg subtype.val $ @H ⟨a, as⟩ ⟨b, bs⟩ h⟩
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- lemma inj_on_preimage {B : set (set β)} (hB : B ⊆ powerset (range f)) :
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+ lemma inj_on_preimage {B : set (set β)} (hB : B ⊆ 𝒫 (range f)) :
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inj_on (preimage f) B :=
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λ s hs t ht hst, (preimage_eq_preimage' (hB hs) (hB ht)).1 hst
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@@ -436,7 +436,7 @@ theorem left_inv_on.inj_on (h : left_inv_on f₁' f s) : inj_on f s :=
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calc
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x₁ = f₁' (f x₁) : eq.symm $ h h₁
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... = f₁' (f x₂) : congr_arg f₁' heq
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- ... = x₂ : h h₂
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+ ... = x₂ : h h₂
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theorem left_inv_on.surj_on (h : left_inv_on f' f s) (hf : maps_to f s t) : surj_on f' t s :=
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λ x hx, ⟨f x, hf hx, h hx⟩
@@ -475,7 +475,7 @@ theorem left_inv_on.image_image (hf : left_inv_on f' f s) :
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f' ' ' (f '' s) = s :=
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by rw [image_image, image_congr hf, image_id']
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- theorem left_inv_on.image_image' (hf : left_inv_on f' f s) (hs : s₁ ⊆ s) :
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+ theorem left_inv_on.image_image' (hf : left_inv_on f' f s) (hs : s₁ ⊆ s) :
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f' ' ' (f '' s₁) = s₁ :=
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(hf.mono hs).image_image
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