DFinsupp Infinite not Finite
Obelix.PartialSolution.DFinsuppInfinite_not_Finite
Plain-language statement
The module Π₀ _ : ℕ, ℤ is not a finite rank module over ℤ
Exact Lean statement
theorem DFinsuppInfinite_not_Finite : ¬(Module.Finite ℤ A)
Formal artifact
Lean source
theorem DFinsuppInfinite_not_Finite : ¬(Module.Finite ℤ A) := by /- Prove by giving a series of Module equivalences (LinearEquiv's) between DFinsupp, Finsupp, and finally Polynomial, where we can appeal to Polynomial.not_finite to do the lifting for us. -/ have f : (Polynomial ℤ) ≃ₗ[ℤ] (Finsupp ℕ ℤ) := { toFun := Polynomial.toFinsupp invFun := Polynomial.ofFinsupp map_add' _ _ := by simp; rfl map_smul' := by intros rw [zsmul_eq_mul, eq_intCast, Int.cast_id, ← zsmul_eq_mul] rfl left_inv := by simp [Function.LeftInverse] right_inv := by simp [Function.RightInverse, Function.LeftInverse] } rw [← Module.Finite.equiv_iff (finsuppLequivDFinsupp ℤ), ← Module.Finite.equiv_iff f] exact Polynomial.not_finite- Project
- Equational Theories
- License
- Apache-2.0
- Commit
- 7e276a2d05e8
- Source
- equational_theories/Obelix.lean:71-87
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Person-level attribution pending.
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Person-level attribution pending.