20 lines
560 B
Text
20 lines
560 B
Text
import data.nat.basic
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open nat
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structure s1 (A : Type) :=
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(x : A) (y : A) (h : x = y)
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structure s2 (A : Type) :=
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(mul : A → A → A) (one : A)
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structure s3 (A : Type) extends s1 A, s2 A :=
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(mul_one : ∀ a : A, mul a one = a)
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definition v1 : s1 nat := {| s1, x := 10, y := 10, h := rfl |}
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definition v2 : s2 nat := {| s2, mul := nat.add, one := zero |}
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definition v3 : s3 nat := {| s3, mul_one := add_zero, v1, v2 |}
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example : s3.x v3 = 10 := rfl
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example : s3.y v3 = 10 := rfl
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example : s3.mul v3 = nat.add := rfl
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example : s3.one v3 = nat.zero := rfl
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