Definitions NuprlPrimitives Sections NuprlLIB Doc
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The last subgoal of the proof of Thm* A  Top,

1. A : Type
2. x : A
  x  Top

does not simply mean that every notation of (supposed) type A is also a notation of type Top.

It means further that if a = b  A then a = b  Top.

About:
universeequalmembersubtypetoppfdisp_conclred_hyp
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Definitions NuprlPrimitives Sections NuprlLIB Doc