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[AUGER Cédric <sedrikov AT gmail.com>]

Hi all, is there any reason to have proj1 and proj2 opaque?

I do not really see the point in doing so.
Making them transparent wouldn't break proof-irrelevance, and would
allow simplifications where conj is involved.

Maybe I shouldn't do some computation inside of Prop, but really I do
not understand why forbiding "proj1 (conj a b)" to reduce to "a".

Plus, in the source code,

  Theorem proj1 : A /\ B -> A.
  Proof.
    destruct 1; trivial.
  Qed.

use of tactics here could be considered as obfuscation, it is longer to
write than direct access and less evident.

Record and (A B : Prop) : Prop := conj { proj1 : A; proj2 : B }.

Would be a lot more compact.

I was pretty sure, that "proj1 (conj a b)" used to reduce to "a" (with
a transparent definition of proj1 of course).