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Mathlib/CategoryTheory/Shift/CommShiftTwo.lean

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -66,7 +66,7 @@ noncomputable def CommShift₂Setup.int [Preadditive D] [HasShift D ℤ]
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assoc _ _ _ := by
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dsimp
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rw [← zpow_add, ← zpow_add]
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cutsat
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lia
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commShift _ _ := ⟨by cat_disch⟩
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ε p q := (-1) ^ (p * q)
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Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup/FinTwo.lean

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -55,7 +55,7 @@ lemma isParabolic_iff_of_upperTriangular [IsReduced R] (hm : m 1 0 = 0) :
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have aux : m.discr = 0 ↔ m 0 0 = m 1 1 := by
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suffices m.discr = (m 0 0 - m 1 1) ^ 2 by
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rw [this, IsReduced.pow_eq_zero_iff two_ne_zero, sub_eq_zero]
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grind [disc_fin_two, trace_fin_two, det_fin_two]
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grind [discr_fin_two, trace_fin_two, det_fin_two]
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have (h : m 0 0 = m 1 1) : m ∈ Set.range (scalar _) ↔ m 0 1 = 0 := by
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constructor
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· rintro ⟨a, rfl⟩

Mathlib/RingTheory/IntegralClosure/Algebra/Ideal.lean

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -96,7 +96,7 @@ lemma exists_monic_aeval_eq_zero_forall_mem_of_mem_map [Algebra.IsIntegral R S]
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obtain ⟨p, hp, e, h⟩ := exists_monic_aeval_eq_zero_forall_mem_pow_of_mem_map hx
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refine ⟨p, hp, e, fun i hi ↦ ?_⟩
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obtain hi | hi := hi.lt_or_gt
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· exact Ideal.pow_le_self (by cutsat) (h _)
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· exact Ideal.pow_le_self (by lia) (h _)
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· simp [coeff_eq_zero_of_natDegree_lt hi]
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end Polynomial

Mathlib/RingTheory/Perfection.lean

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -194,14 +194,14 @@ theorem coeff_surjective (h : Function.Surjective (frobenius R p)) (n : ℕ) :
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choose x hx using h xk
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use x
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· intro m
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obtain (h1 | h1 | h1) : n ≤ m ∨ n = m + 1 ∨ ¬ n ≤ m + 1 := by cutsat
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· have h1' : n ≤ m + 1 := by cutsat
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obtain (h1 | h1 | h1) : n ≤ m ∨ n = m + 1 ∨ ¬ n ≤ m + 1 := by lia
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· have h1' : n ≤ m + 1 := by lia
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simp only [h1', ↓reduceDIte, h1, Nat.leRec_succ, ← frobenius_def]
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exact Classical.choose_spec (h _)
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· subst h1
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simp [← frobenius_def]
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· have h1' : ¬ n ≤ m := by cutsat
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have : n - m = (n - (m + 1)) + 1 := by cutsat
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· have h1' : ¬ n ≤ m := by lia
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have : n - m = (n - (m + 1)) + 1 := by lia
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simp [h1, h1', this, pow_succ, pow_mul]
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· simp
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