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[Coq-Club] another question (Prop as a subtype of Set)

From: Vladimir Voevodsky <vladimir AT ias.edu>
To: Coq Club <coq-club AT pauillac.inria.fr>
Subject: [Coq-Club] another question (Prop as a subtype of Set)
Date: Tue, 13 Oct 2009 13:49:08 -0400
List-archive: <http://pauillac.inria.fr/pipermail/coq-club/>

In the following sequence of instructions:

Axiom f5 : Set -> nat .

Axiom P0 : Prop .

Axiom S0 : Set .

Check f5 P0 .

Check eq P0 S0 .

The last two produce the following reactions:

f5 P0
: nat

and

Error: The term "S0" has type "Set" while it is expected to have type "Prop".

respectively.

Why does f5 treat Prop as a subtype of Set but eq does not?

V.

Re: [Coq-Club] an inductive types question, (continued)