30 lines
927 B
Text
30 lines
927 B
Text
module
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open Lean.Grind
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example {α} [CommRing α] [IsCharP α 0]
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(d t : α)
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(Δ40 : d + t + d * t = 0)
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(Δ41 : d + d * t - 2 * d * t^2 + d * t^4 + d^2 * t^4 = 0) :
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t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by grind
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example {α} [CommRing α] [IsCharP α 0]
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(d t d_inv : α)
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(Δ40 : d * (d + t + d * t) = 0)
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(Δ41 : d * (d + d * t - 2 * d * t^2 + d * t^4 + d^2 * t^4) = 0)
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(_ : d * d_inv = 1) :
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t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by grind
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-- The theorems above hold in any `CommRing`
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example {α} [CommRing α]
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(d t : α)
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(Δ40 : d + t + d * t = 0)
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(Δ41 : d + d * t - 2 * d * t^2 + d * t^4 + d^2 * t^4 = 0) :
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t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by grind
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example {α} [CommRing α]
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(d t d_inv : α)
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(Δ40 : d * (d + t + d * t) = 0)
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(Δ41 : d * (d + d * t - 2 * d * t^2 + d * t^4 + d^2 * t^4) = 0)
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(_ : d * d_inv = 1) :
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t + 2 * t^2 - t^3 - 2 * t^4 + t^5 = 0 := by grind
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