PrintForm Definitions myhill nerode Sections AutomataTheory Doc

At: total back listify 1 1
1. Alph: Type
2. S: ActionSet(Alph)
3. sL: S.car*
4. Fin(Alph)
5. Fin(S.car)

n:. TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))
By:
Analyze 0
THEN
NatInd -1
Generated subgoals:

1 TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = 0 & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))
26. n:
7. 0 < n
8. TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n-1 & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))
TBL:S.car*. (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) ||TBL|| = n & (i:||TBL||, j:i. TBL[i] = TBL[j]) & (s:S.car. mem_f(S.car;s;TBL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (AL:S.car*. (s:S.car. mem_f(S.car;s;AL) (w:Alph*. mem_f(S.car;(S:ws);sL))) & (s:S.car. mem_f(S.car;s;sL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)) & (s:S.car, a:Alph. mem_f(S.car;S.act(a,s);TBL) mem_f(S.car;s;TBL) mem_f(S.car;s;AL)))

About:
allexistslistorand
equalnatural_numberimpliesapplyuniverse