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tweak arguments
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mariainesdff committed Oct 17, 2024
1 parent cdb156e commit 65a4761
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6 changes: 3 additions & 3 deletions DividedPowers/Basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -158,13 +158,13 @@ theorem dpow_smul' (n : ℕ) (a : A) {x : A} (hx : x ∈ I) :
simp only [smul_eq_mul, hI.dpow_smul, hx]

@[simp]
theorem dpow_mul_right (n : ℕ) (a : A) {x : A} (ha : x ∈ I) :
theorem dpow_mul_right {n : ℕ} {a : A} {x : A} (ha : x ∈ I) :
hI.dpow n (x * a) = hI.dpow n x * a ^ n := by
rw [mul_comm, hI.dpow_smul n ha, mul_comm]

theorem dpow_smul_right (n : ℕ) (a : A) {x : A} (hx : x ∈ I) :
theorem dpow_smul_right {n : ℕ} {a : A} {x : A} (hx : x ∈ I) :
hI.dpow n (x • a) = hI.dpow n x • a ^ n := by
rw [smul_eq_mul, hI.dpow_mul_right n a hx, smul_eq_mul]
rw [smul_eq_mul, hI.dpow_mul_right hx, smul_eq_mul]

theorem factorial_mul_dpow_eq_pow {n : ℕ} {x : A} (hx : x ∈ I) :
(n.factorial : A) * hI.dpow n x = x ^ n := by
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2 changes: 1 addition & 1 deletion DividedPowers/DPAlgebra/Dpow.lean
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Expand Up @@ -1113,7 +1113,7 @@ theorem roby_prop_4
· exact Ideal.mul_mem_left _ _ hy
· exact Ideal.mul_mem_right _ _ hc
· intro n hn
rw [hI.dpow_mul_right n hc]
rw [hI.dpow_mul_right hc]
apply Ideal.mul_mem_left
rw [← Nat.succ_pred_eq_of_ne_zero hn, pow_succ]
apply Ideal.mul_mem_left _ _ hy
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6 changes: 3 additions & 3 deletions DividedPowers/IdealAdd.lean
Original file line number Diff line number Diff line change
Expand Up @@ -368,7 +368,7 @@ theorem dpow_comp_aux {J : Ideal A} (hJ : DividedPowers J)
Nat.multinomial (Finset.range (n + 1)) fun i : ℕ => Multiset.count i ↑x * (n - i)) *
hI.dpow p a *
hJ.dpow (m * n - p) b := by
rw [dpow_eq hI hJ hIJ n ha hb, dpow_sum_aux (dpow hI hJ)]
rw [dpow_eq hI hJ hIJ n ha hb, dpow_sum_aux (dpow := dpow hI hJ)]
have L1 :
∀ (k : Sym ℕ m) (i : ℕ) (_ : i ∈ Finset.range (n + 1)),
dpow hI hJ (Multiset.count i ↑k) (hI.dpow i a * hJ.dpow (n - i) b) =
Expand Down Expand Up @@ -398,7 +398,7 @@ theorem dpow_comp_aux {J : Ideal A} (hJ : DividedPowers J)
· rw [if_neg hi1]; rw [if_neg hi2]
rw [mul_comm, dpow_smul hI hJ hIJ, mul_comm]
rw [dpow_eq_of_mem_left hI hJ hIJ _ (hI.dpow_mem hi1 ha)]
rw [← hJ.factorial_mul_dpow_eq_pow (Multiset.count i k)]
rw [← hJ.factorial_mul_dpow_eq_pow]
rw [hI.dpow_comp _ hi1 ha]
rw [hJ.dpow_comp _ hi2' hb]
simp only [← mul_assoc]; apply congr_arg₂ _ _ rfl
Expand Down Expand Up @@ -523,7 +523,7 @@ theorem dpow_comp_coeffs {m n p : ℕ} (hn : n ≠ 0) (hp : p ≤ m * n) :
let h1 : (1 : A) ∈ I := Submodule.mem_top
let hX : X ∈ I := Submodule.mem_top

rw [← hI.factorial_mul_dpow_eq_pow (m * n) (X + 1) Submodule.mem_top]
rw [← hI.factorial_mul_dpow_eq_pow Submodule.mem_top]
rw [← Polynomial.coeff_C_mul]
rw [← mul_assoc, mul_comm (C ((Nat.uniformBell m n) : ℚ)), mul_assoc]
simp only [C_eq_natCast]
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