 } == {k:
} == {k: | i
| i  k  <  j }
 k  <  j }
 Thm*  n:
n: , f:(
, f:( n
n

 n). Surj(
n). Surj( n;
n;  n; f)
n; f) 
 Inj(
 Inj( n;
n;  n; f)    surj_is_inj
n; f)    surj_is_inj
 Thm*  q:
q: , E:(
, E:( q*
q*

 q*
q*
 Prop).
 (EquivRel x,y:
Prop).
 (EquivRel x,y: q*. x E y)  &  (
q*. x E y)  &  ( x,y:
x,y: q*. Dec(x E y))
q*. Dec(x E y)) 
 (
 
 ( h:(
h:( q*
q*

 q*). 
 (
q*). 
 ( x,y:
x,y: q*. (x E y)
q*. (x E y) 
 h(x) = h(y))  &  (
 h(x) = h(y))  &  ( x:
x: q*. x E (h(x))))
 
 list_quo_choice
q*. x E (h(x))))
 
 list_quo_choice
 Thm*  q:
q: , x:
, x: q*. q = 0
q*. q = 0 
 x = nil    empty_alph_list
 x = nil    empty_alph_list
 Thm*  q:
q:
 , E:(
, E:( q*
q*

 q*
q*
 Prop).
 (EquivRel x,y:
Prop).
 (EquivRel x,y: q*. x E y)  &  (
q*. x E y)  &  ( x,y:
x,y: q*. Dec(x E y))
q*. Dec(x E y)) 
 (
 
 ( h:(
h:( q*
q*

 q*). 
 (
q*). 
 ( x,y:
x,y: q*. (x E y)
q*. (x E y) 
 h(x) = h(y))  &  (
 h(x) = h(y))  &  ( x:
x: q*. x E (h(x))))
 
 list_quo_choice_pls
q*. x E (h(x))))
 
 list_quo_choice_pls
In prior sections: int 1 bool 1 choice 1 int 2 list 1 finite sets list 3 autom exponent relation autom det automata myhill nerode