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chore: run mk_all to register BinomialType and DeltaOperator
1 parent 7b31b50 commit a84f277

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Lines changed: 13 additions & 8 deletions

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Mathlib.lean

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@@ -6496,6 +6496,8 @@ public import Mathlib.RingTheory.HahnSeries.Summable
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public import Mathlib.RingTheory.HahnSeries.Valuation
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public import Mathlib.RingTheory.Henselian
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public import Mathlib.RingTheory.HopfAlgebra.Basic
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public import Mathlib.RingTheory.HopfAlgebra.BinomialType
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public import Mathlib.RingTheory.HopfAlgebra.DeltaOperator
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public import Mathlib.RingTheory.HopfAlgebra.GroupLike
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public import Mathlib.RingTheory.HopfAlgebra.MonoidAlgebra
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public import Mathlib.RingTheory.HopfAlgebra.Polynomial

Mathlib/RingTheory/HopfAlgebra/DeltaOperator.lean

Lines changed: 11 additions & 8 deletions
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@@ -408,10 +408,11 @@ private theorem coeff_taylor_sub_eq (g : R[X])
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simp only [zero_add, Nat.choose_self, Nat.cast_one, one_mul,
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show 1 + (g.natDegree - 1) = g.natDegree from by omega,
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add_sub_cancel_left, leadingCoeff]
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congr 1; push_cast; congr 1
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congr 1; congr 1
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rw [show g.natDegree = g.natDegree - 1 + 1 from by omega]
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simp [Nat.choose_succ_self_right]
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set_option linter.unusedSectionVars false in
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/-- `Q` applied to a polynomial of degree `< N` gives degree `≤ N - 2`. -/
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private theorem natDegree_Q_of_bounded
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{Q : R[X] →ₗ[R] R[X]} {p : R[X]} {N : ℕ}
@@ -457,7 +458,7 @@ private theorem natDegree_delta_op_pow
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| n + 2, _ =>
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set m := n + 2
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set g := Q (X ^ m)
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by_contra hbig; push_neg at hbig
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by_contra hbig; push Not at hbig
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have hg_ne : g ≠ 0 :=
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ne_zero_of_natDegree_gt (by omega)
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have htf : IsAddTorsionFree R := instTorsionFree
@@ -528,11 +529,12 @@ private theorem natDegree_delta_op_pow
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omega
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rw [diff_eq] at hnd_lb; omega
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set_option linter.unusedSectionVars false in
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/-- Over a ℚ-algebra, `natDegree (taylor a p - p) ≤ natDegree p - 1`. -/
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private theorem natDegree_taylor_sub_le (a : R) (p : R[X])
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(hp : 1 ≤ p.natDegree) :
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(taylor a p - p).natDegree ≤ p.natDegree - 1 := by
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by_contra h; push_neg at h
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by_contra h; push Not at h
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have hbound : (taylor a p - p).natDegree ≤ p.natDegree :=
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(natDegree_sub_le _ _).trans
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(by rw [natDegree_taylor, max_self])
@@ -584,14 +586,13 @@ private theorem eval_determines (p : R[X])
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private theorem sum_hasseDeriv_eq_zero
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{Q : R[X] →ₗ[R] R[X]}
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(hse : ∀ a : R, Q.comp (taylor a) = (taylor a).comp Q)
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(hkc : ∀ r : R, Q (C r) = 0)
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(_hkc : ∀ r : R, Q (C r) = 0)
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{f : R[X]} (hQf : Q f = 0) :
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(range (f.natDegree + 1)).sum
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(fun k => (Q (X ^ k)).eval 0 • hasseDeriv k f) =
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0 := by
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apply eval_determines; intro a
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simp only [eval_finset_sum, eval_smul, smul_eq_mul,
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eval_zero]
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simp only [eval_finsetSum, eval_smul, smul_eq_mul]
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have hQta : Q (taylor a f) = 0 := by
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have := congr_arg (· f) (hse a)
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simp only [LinearMap.comp_apply] at this
@@ -611,7 +612,7 @@ private theorem sum_hasseDeriv_eq_zero
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exact Q.map_smul _ _
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have h0 :=
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congr_arg (Polynomial.eval 0) (hdecomp ▸ hQta)
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simp only [eval_finset_sum, eval_smul, smul_eq_mul,
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simp only [eval_finsetSum, eval_smul, smul_eq_mul,
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eval_zero] at h0
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convert h0 using 1; apply Finset.sum_congr rfl
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intro k _
@@ -744,13 +745,14 @@ private theorem taylor_basic_eq
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rw [hQ_lhs, hQ_rhs, ih]
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· -- D.eval 0 = 0
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rw [eval_sub, taylor_eval, zero_add,
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sub_eq_zero, eval_finset_sum]
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sub_eq_zero, eval_finsetSum]
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rw [Finset.sum_eq_single_of_mem 0
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(Finset.mem_range.mpr (by omega))]
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· simp [hp.zero_one, Nat.choose_zero_right]
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· intro k _ hk
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simp [hp.normalized k (by omega : 0 < k)]
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set_option linter.unusedSectionVars false in
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/-- The composition `lmul' ∘ (id ⊗ aeval(C a)) ∘ Δ` equals `taylor a`
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as algebra homs. -/
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private theorem comul_taylor_bridge (a : R) :
@@ -766,6 +768,7 @@ private theorem comul_taylor_bridge (a : R) :
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Algebra.TensorProduct.lmul'_apply_tmul,
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taylor_X]
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set_option linter.unusedSectionVars false in
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/-- `aeval (C a) g = C (g.eval a)`. -/
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private theorem aeval_C_eq_C_eval (a : R)
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(g : R[X]) :

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