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Fix typos
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Mathlib/Combinatorics/SimpleGraph/Extremal/Zarankiewicz.lean

Lines changed: 2 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -95,7 +95,7 @@ theorem lt_zarankiewicz_iff
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variable {R : Type*} [Semiring R] [LinearOrder R] [FloorSemiring R]
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@[inherit_doc zarankiewicz_le_iff]
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theorem zarankiewicz_card_le_iff_of_nonneg
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theorem zarankiewicz_le_iff_of_nonneg
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(hm : card V = m) (hn : card W = n) (hs : card α = s) (ht : card β = t) {x : R} (h : 0 ≤ x) :
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zarankiewicz m n s t ≤ x ↔
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∀ ⦃G : SimpleGraph (V ⊕ W)⦄ [DecidableRel G.Adj], G ≤ completeBipartiteGraph V W →
@@ -104,7 +104,7 @@ theorem zarankiewicz_card_le_iff_of_nonneg
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exact zarankiewicz_le_iff hm hn hs ht ⌊x⌋₊
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@[inherit_doc lt_zarankiewicz_iff]
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theorem lt_zarankiewicz_card_iff_of_nonneg
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theorem lt_zarankiewicz_iff_of_nonneg
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(hm : card V = m) (hn : card W = n) (hs : card α = s) (ht : card β = t) {x : R} (h : 0 ≤ x) :
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x < zarankiewicz m n s t ↔
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∃ G : SimpleGraph (V ⊕ W), ∃ _ : DecidableRel G.Adj, G ≤ completeBipartiteGraph V W ∧
@@ -142,7 +142,6 @@ theorem two_mul_extremalNumber_le_zarankiewicz_symm
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· simp_rw [mem_filter, mem_univ, true_and]
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refine ⟨bipartiteDoubleCover_le, ?_⟩
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contrapose! h
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rw [not_free] at h ⊢
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refine completeBipartiteGraph_isContained_bipartiteDoubleCover.mp <|
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h.trans' ⟨Iso.toCopy ?_⟩
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exact completeBipartiteGraphCongr

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