At: mn  23  lem 1 2 2 1 1
1. Alph: Type
2. R: Alph*
 Alph*
Alph*
 Prop
Prop
3. Fin(Alph)
4. EquivRel x,y:Alph*. x R y
5. Fin(x,y:Alph*//(x R y))
6.  x,y,z:Alph*. (x R y)
x,y,z:Alph*. (x R y) 
 ((z @ x) R (z @ y))
 ((z @ x) R (z @ y))
7. g: (x,y:Alph*//(x R y))


8. Fin((x,y:Alph*//(x R y)) (x,y:Alph*//(x R y)))
(x,y:Alph*//(x R y)))
9.  a:Alph, x:x,y:Alph*//(x R y). a.x
a:Alph, x:x,y:Alph*//(x R y). a.x  x,y:Alph*//(x R y)
 x,y:Alph*//(x R y)
10.  fL:((x,y:Alph*//(x R y))
fL:((x,y:Alph*//(x R y)) (x,y:Alph*//(x R y)))*.
(x,y:Alph*//(x R y)))*. 
 t:((x,y:Alph*//(x R y))
t:((x,y:Alph*//(x R y)) (x,y:Alph*//(x R y))). 
(
(x,y:Alph*//(x R y))). 
( x.x/x1,x2.
x.x/x1,x2.
 (g(x1)) =
(g(x1)) = (g(x2)))(t)
 (g(x2)))(t) 
 mem_f((x,y:Alph*//(x R y))
 mem_f((x,y:Alph*//(x R y)) (x,y:Alph*//(x R y));t;fL)
(x,y:Alph*//(x R y));t;fL)
11. a: Alph
12. xy: (x,y:Alph*//(x R y)) (x,y:Alph*//(x R y))
(x,y:Alph*//(x R y))
13. x: x,y:Alph*//(x R y)
14. y: x,y:Alph*//(x R y)
15. xy =  < x,y > 
  a.x
 a.x  x,y:Alph*//(x R y)
 x,y:Alph*//(x R y)
By: BackThru 9
Generated subgoals:None
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