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Suppose I define this set.

Inductive Set_1 : Set :=
  | Constr_1 : Set_1
  | Constr_2 : Set_1.

Is it possible to prove this statement?

(Constr_1 = Constr_2) = False

If so, what tactics do I use? This might be useful for autorewrite.

  • possible duplicate of [how can this be proved in coq?](http://stackoverflow.com/questions/11071165/how-can-this-be-proved-in-coq) –  Jan 20 '13 at 11:53

1 Answers1

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(A <-> B) -> A = B is called propositional extensionality and is implied by classical logic.

But you don't need it for using equivalences with autorewrite, just Require Import Coq.Setoids.Setoid.