Nuprl - Pf mn_23_lem_1 1 1 1 2 1 1 2 2 1 1 2 4 1

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At: mn 23 lem 1 1 1 1 2 1 1 2 2 1 1 2 4 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. x2: x,y:Alph*//(x R y)
13. x3: x,y:Alph*//(x R y)
14. y1: Alph*
15. u: Alph
16. v: Alph*
17. ( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :v < x2,x3 > ) = ( < x2,x3 > /x1,x2. < v@x1,v@x2 > )

u.(v @ x2) = u.(v @ x2) x,y:Alph*//(x R y)

By: Analyze 12 THEN Analyze

Generated subgoal:

1 18. x4: Alph*
19. x5: Alph*
20. x4 R x5
(u.(v @ x4)) R (u.(v @ x5))

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