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1. Alph: Type
2. R: Alph*Alph*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) ((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)))
9. a:Alph, x:x,y:Alph*//(x R y). a.x x,y:Alph*//(x R y)
10. fL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
11. < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,xy. xy/x,y. < a.x,a.y > > ActionSet(Alph)
12. TBL: ((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. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))

Dec(x@0:Alph*. (g(x@0@x) g(x@0@y)))
By:
Assert (w:Alph*. (g(w@x) g(w@y)) (g(w@x)) = (g(w@y)))
THEN
RWH (HypC -1) 0
THEN
Thin -1
Generated subgoals:

115. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))
16. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))
17. w: Alph*
18. (g(w@x) g(w@y))
(g(w@x)) = (g(w@y))
215. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))
16. mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)); < x,y > ;TBL) (w:Alph*. (g(w@x)) = (g(w@y)))
17. w: Alph*
18. (g(w@x)) = (g(w@y))
(g(w@x) g(w@y))
3 Dec(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)))

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