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Finish the PolyType_0 lemma!

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chelseaandmadrid 2023-06-15 15:38:25 -07:00
parent 007e8cf795
commit 300007621a
1 changed files with 7 additions and 37 deletions
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44
CommAlg/final_poly_type.lean
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@ -198,6 +198,8 @@ lemma PolyType_0 (f : ℤ → ℤ) : (PolyType f 0) ↔ (∃ (c : ℤ), ∃ (N :
have H22 := λ n=> (hh n).right
have H2 : c ≠ 0 := by
exact H22 0
have H2 : (c : ℚ) ≠ 0 := by
simp; tauto
clear H22
constructor
· intro n Nn
@ -206,47 +208,15 @@ lemma PolyType_0 (f : ℤ → ℤ) : (PolyType f 0) ↔ (∃ (c : ℤ), ∃ (N :
tauto
rw [this]
have this2 : Polynomial.eval (n : ℚ) Poly = (c : ℚ) := by
have this3 : ∀ r : ℚ, (Polynomial.eval r Poly) = (c : ℚ) := (Poly_constant Poly (c : ℚ)).mp rfl
have this3 : ∀ r : ℚ, (Polynomial.eval r Poly) = (c : ℚ) := (Poly_constant Poly (c : ℚ)).mp rfl
exact this3 n
exact this2.symm
· sorry
-- intro n
-- specialize aaa n
-- have this1 : c ≠ 0 → f n = c := by
-- sorry
-- rcases aaa with ⟨A, B⟩
-- have this1 : f n = c := by
-- tauto
-- constructor
-- clear A
-- · have this2 : ∀ (t : ℚ), (Polynomial.eval t Poly) = (c : ℚ) := by
-- rw [← Poly_constant Poly (c : ℚ)]
-- sorry
-- specialize this2 n
-- rw [this2]
-- tauto
-- · sorry
-- constructor
-- · intro n Nn
-- specialize aaa n
-- have this1 : c ≠ 0 → f n = c := by
-- tauto
-- rcases aaa with ⟨A, B⟩
-- have this1 : f n = c := by
-- tauto
-- clear A
-- have this2 : ∀ (t : ℚ), (Polynomial.eval t Poly) = (c : ℚ) := by
-- rw [← Poly_constant Poly (c : ℚ)]
-- sorry
-- specialize this2 n
-- rw [this2]
-- tauto
-- · sorry
· have this : Polynomial.degree Poly = 0 := by
simp only [map_intCast]
exact Polynomial.degree_C H2
tauto