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pimotteEtienneC30
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Co-authored-by: Etienne <66847262+EtienneC30@users.noreply.github.com>
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Mathlib/Data/Set/Quot.lean

Lines changed: 5 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -45,8 +45,8 @@ lemma out_image_represents (C : Set (Quot r)) : (Quot.out '' C).Represents C whe
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rw [← hyc, c'.out_eq]
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exact {c} h := by
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ext v
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simp only [mem_inter_iff, mem_image, mem_empty_iff_false, iff_false,
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not_and, forall_exists_index, and_imp]
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simp only [mem_inter_iff, mem_image, mem_empty_iff_false, iff_false, not_and,
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forall_exists_index, and_imp]
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intro c' hc' hv hvc
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rw [← hvc, ← hv, c'.out_eq] at h
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exact h hc'
@@ -67,12 +67,11 @@ lemma disjoint_represents (hrep : s.Represents C) (h : c ∉ C) : Disjoint s c :
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lemma ncard_sdiff_represents_of_mem [Fintype α] (hrep : s.Represents C) (h : c ∈ C) :
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((c : Set α) \ s).ncard = (c : Set α).ncard - 1 := by
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simp [← ncard_inter_add_ncard_diff_eq_ncard c s (toFinite _),
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inter_comm, ncard_represents_inter hrep h]
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simp [← ncard_inter_add_ncard_diff_eq_ncard c s (toFinite _), inter_comm,
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ncard_represents_inter hrep h]
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lemma ncard_sdiff_represents_of_not_mem [Fintype α] (hrep : s.Represents C) (h : c ∉ C) :
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((c : Set α) \ s).ncard = (c : Set α).ncard := by
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simp [← ncard_inter_add_ncard_diff_eq_ncard c s (toFinite _),
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inter_comm, hrep.exact h]
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simp [← ncard_inter_add_ncard_diff_eq_ncard c s (toFinite _), inter_comm, hrep.exact h]
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end Set

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