Condition block scoping

Question

I have a list of functional rules of the type F[x_]:=y;cond[x] with always the same condition. The list is long and rule 1 of programming says: "Do not copy!" I surely can somehow "extract" my condition?!

fromherecondmusthold statement
F[x_]:=y; (*if cond[x]*)
G[x_]:=z; (*if cond[x]*)
fromherecondmustnolongerhold statement

As you see, a slight snag would be that F[u_]:=v would not match the pattern, although an underscored variable is a bound one that could have any other name.

Answer 1

As an example we choose a condition x>0:

ClearAll[f1, f2];
With[{y = x_ /; x > 0},
 f1[y] = x;
 f2[y] = 2 x;
 ]

Now to test:

f1[-1]
(*f1[-1]*)
f1[1]
(*1*)
f2[-1]
(*f2[-1]*)
f2[1]
(*2*)