| Some definitions of interest. |
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habs_list | Def abs_list == r:(  'a) . @a:'a List. (r = rep_list('a;a)) |
| | Thm* 'a:S. abs_list (hprod((hnum  'a); hnum)  hlist('a)) |
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his_list_rep | Def is_list_rep
Def == r:(  'a) .  f:  'a
Def == r:(  'a) .    n:
Def == r:(  'a) .    (r
Def == r:(  'a) .    = < m: . if m< n then f(m) else @ x:'a. true fi ,n>) |
| | Thm* 'a:S. is_list_rep (hprod((hnum  'a); hnum)  hbool) |
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iso_pair | Def iso_pair('a;'b;P;rep;abs)
Def == ( r:'b. abs(r) = (@a:'a. (r = rep(a)))) & type_definition('b;'a;P;rep) |
| | Thm* 'a,'b:S, P:('b  ), rep:('a 'b), abs:('b 'a).
Thm* iso_pair('a;'b;P;rep;abs) Prop |
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choose | Def @x:T. P(x) == InjCase(lem({x:T| P(x) }); x. x, arb(T)) |
| | Thm* T:S, P:(T Type). (@x:T. P(x)) T |
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hrep_list | Def rep_list == l:'a List. rep_list('a;l) |
| | Thm* 'a:S. rep_list (hlist('a)  hprod((hnum  'a); hnum)) |
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nat | Def == {i: | 0 i } |
| | Thm* Type |
| | Thm* S |
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stype | Def S == {T:Type| x:T. True } |
| | Thm* S Type{2} |
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type_definition | Def type_definition('a;'b;P;rep)
Def == ( x',x'':'b. rep(x') = rep(x'') 'a  x' = x'')
Def == & ( x:'a. (P(x))  ( x':'b. x = rep(x'))) |
| | Thm* 'a,'b:Type, P:('a  ), rep:('b 'a). type_definition('a;'b;P;rep) Prop |