11 lines
573 B
Text
11 lines
573 B
Text
protected def rel : ℤ × ℤ → ℤ × ℤ → Prop
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| ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ := n₁ * d₂ = n₂ * d₁
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private def mul' : ℤ × ℤ → ℤ × ℤ → ℤ × ℤ
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| ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ := ⟨n₁ * n₂, d₁ * d₂⟩
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example : ∀(a b c d : ℤ × ℤ), rel a c → rel b d → rel (mul' a b) (mul' c d) :=
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λ⟨n₁, d₁⟩ ⟨n₂, d₂⟩ ⟨n₃, d₃⟩ ⟨n₄, d₄⟩,
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assume (h₁ : n₁ * d₃ = n₃ * d₁) (h₂ : n₂ * d₄ = n₄ * d₂),
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show (n₁ * n₂) * (d₃ * d₄) = (n₃ * n₄) * (d₁ * d₂),
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by cc
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