Nuprl - Pf mn_23_lem_1 1 1 1 2 1 1 2 2 2 2 1 1 1

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At: mn 23 lem 1 1 1 1 2 1 1 2 2 2 2 1 1 1

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. x: x,y:Alph*//(x R y)
9. y: x,y:Alph*//(x R y)
10. < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > ActionSet(Alph)
11. Fin((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))
12. x:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))), y:Alph*. ( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :yx) = (x/x1,x2. < y@x1,y@x2 > )
13. RL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*
14. s:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (w:Alph*. ( < x,y > /x1,x2. < w@x1,w@x2 > ) = s) mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));s;RL)

(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false) (p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;RL))

By: GenRepD

Generated subgoals:

1 15. x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false
p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;RL)

2 15. p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));p;RL)
x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false

About:

1	15. `x@0:Alph. (g(x@0@x)) = (g(x@0@y)) = false` `p:((x,y:Alph//(x R y))(x,y:Alph//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph//(x R y))(x,y:Alph*//(x R y));p;RL)`
2	15. `p:((x,y:Alph//(x R y))(x,y:Alph//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & mem_f((x,y:Alph//(x R y))(x,y:Alph//(x R y));p;RL)` `x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false`