47 lines
774 B
Text
47 lines
774 B
Text
import logic
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namespace N1
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variable num : Type.{1}
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variable foo : num → num → num
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end N1
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namespace N2
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variable val : Type.{1}
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variable foo : val → val → val
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end N2
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using N1
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using N2
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variables a b : num
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variables x y : val
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check foo a b
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check foo x y
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variable f : num → val
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coercion f
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check foo a x
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check foo x y
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check foo x a
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check foo a b
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theorem T1 : foo a b = N1.foo a b
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:= refl _
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definition aux1 := foo a b -- System elaborated it to N2.foo (f a) (f b)
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theorem T2 : aux1 = N2.foo (f a) (f b)
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:= refl _
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using N1
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definition aux2 := foo a b -- Now N1 is in the beginning of the queue again, and this is elaborated to N1.foo a b
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check aux2
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theorem T3 : aux2 = N1.foo a b
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:= refl aux2
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check foo a b
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theorem T4 : foo a b = N1.foo a b
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:= refl _
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