Tactic to partially compute goal in Coq

Question

I have goal

quad X Y

, but I don't remember definition of "quad" and I don't want to start searching of its definition.

Is there a tactic that allow me rapidly substitute quad with its definition?

 Record quad (X Y:Type):= { x:X; y:Y}.

Or I have to remember and use

refine (@Build_quad _ _).

?

Answer 1

Your slightly mistaken, Build_quad is not the definition of quad , it is its constructor. It creates terms of type quad . As @ejgallego said, you should use the constructor tactic in this situation.

Your goal wants you to provide a term of type quad XY , and the only way to build such a term from scratch is to use the constructor Build_quad of type forall XY: Type, X -> Y -> quad XY .