PrintForm Definitions myhill nerode Sections AutomataTheory Doc

At: mn 23 lem 1 1 1 1 2 1 1 2 2 2 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. 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)),a,p. p/x,y. < a.x,a.y > > .car*. s: < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > .car. (w:Alph*. ( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :w < x,y > ) = s) mem_f( < (x,y:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > .car;s;RL)

Dec(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false)
By:
Reduce -1
THEN
Analyze -1
Generated subgoal:

113. 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:Alph*//(x R y))(x,y:Alph*//(x R y)),a,p. p/x,y. < a.x,a.y > > :w < x,y > ) = s) mem_f((x,y:Alph*//(x R y))(x,y:Alph*//(x R y));s;RL)
Dec(x@0:Alph*. (g(x@0@x)) = (g(x@0@y)) = false)

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