19 lines
586 B
Text
19 lines
586 B
Text
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constant A₁ : Type
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constant A₂ : A₁ → Type
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constant A₃ : Π (a₁ : A₁), A₂ a₁ → Type
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structure foo :=
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mk :: (a₁ : A₁) (a₂ : A₂ a₁) (a₃ : A₃ a₁ a₂)
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theorem foo.eq {a₁ b₁ : A₁} {a₂ : A₂ a₁} {b₂ : A₂ b₁} {a₃ : A₃ a₁ a₂} {b₃ : A₃ b₁ b₂}
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(H₁ : a₁ = b₁) (H₂ : eq.rec_on H₁ a₂ = b₂) (H₃ : eq.rec_on H₂ (eq.rec_on H₁ a₃) = b₃)
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: foo.mk a₁ a₂ a₃ = foo.mk b₁ b₂ b₃ :=
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begin
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cases H₁,
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cases H₂,
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cases H₃,
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apply rfl
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end
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print definition foo.eq
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