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

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At: mn 23 lem 1 1 1 1 2 1 1 2 2 2 2 1 1 2 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. Fin((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))
11. RL: ((x,y:Alph*//(x R y))(x,y:Alph*//(x R y)))*

Dec(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;nil))

By: Reduce 0

Generated subgoal:

1 Dec(p:((x,y:Alph*//(x R y))(x,y:Alph*//(x R y))). (p/p1,p2.(g(p1)) = (g(p2))) = false & False)

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