PrintForm Definitions myhill nerode Sections AutomataTheory Doc

At: mn 23 lem 1 1 1 1 2 1 1 2 2 1 1 2
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 > )

(( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :v < x2,x3 > )/x,y. < u.x,u.y > ) = < u.(v @ x2),u.(v @ x3) > (x,y:Alph*//(x R y))(x,y:Alph*//(x R y))
By:
RWH (HypC -1) 0
THEN
Reduce 0
THEN
Unfold `mn_quo_append` 0
Generated subgoals:

1 (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)) = (x,y:Alph*//(x R y))(x,y:Alph*//(x R y))
218. x4: x,y:Alph*//(x R y)
19. y2: x,y:Alph*//(x R y)
20. ( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :v < x2,x3 > ) = < x4,y2 >
< u.x4,u.y2 > = < u.x4,u.y2 >
3 < u.(v @ x2),u.(v @ x3) > = < u.(v @ x2),u.(v @ x3) > (x,y:Alph*//(x R y))(x,y:Alph*//(x R y))
4 < u.(v @ x2),u.(v @ x3) > = < u.(v @ x2),u.(v @ x3) > (x,y:Alph*//(x R y))(x,y:Alph*//(x R y))

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