196d899c02
This PR adds a monolithic `CommRing` class, for internal use by `grind`, and includes instances for `Int`/`BitVec`/`IntX`/`UIntX`.
20 lines
736 B
Text
20 lines
736 B
Text
class MulOneClass (M : Type u) extends One M, Mul M where
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one_mul : ∀ a : M, 1 * a = a
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mul_one : ∀ a : M, a * 1 = a
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theorem MulOneClass.ext {M : Type u} : ∀ ⦃m₁ m₂ : MulOneClass M⦄, m₁.mul = m₂.mul → m₁ = m₂ := by
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intro m₁ m₂
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cases m₁ with
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| @mk one₁ mul₁ one_mul₁ mul_one₁ =>
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cases one₁ with | mk one₁ =>
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cases mul₁ with | mk mul₁ =>
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cases m₂ with
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| @mk one₂ mul₂ one_mul₂ mul_one₂ =>
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cases one₂ with | mk one₂ =>
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cases mul₂ with | mk mul₂ =>
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simp
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intro h
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cases h
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have := (one_mul₂ one₁).symm.trans (mul_one₁ one₂) -- TODO: make sure we can apply after congr
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subst this
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congr
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