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Project-declaredLean 4.29.1 · mathlib@5e932f97

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

Canonical source
Full Lean sourceLean 4
theorem DFinsuppInfinite_not_Finite : ¬(Module.Finite  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 ) ≃ₗ[] (Finsupp  ) := {    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 ),  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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Plain-language statement

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Source project: Equational Theories

Person-level attribution pending.

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