| Some definitions of interest. |
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habs_num | Def abs_num == n: . @m: . (n = rep_num(m) ) |
| | Thm* abs_num (hind  hnum) |
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hfun | Def 'a  'b == 'a 'b |
| | Thm* 'a,'b:S. ('a  'b) S |
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hind | Def hind ==  |
| | Thm* hind S |
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his_num_rep | Def is_num_rep
Def == m: .  P:  
Def == m: .  ((P(zero_rep)) ( n: . (P(n))  (P(suc_rep(n)))))  (P(m)) |
| | Thm* is_num_rep (hind  hbool) |
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hnum | Def hnum ==  |
| | Thm* hnum S |
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hrep_num | Def rep_num == n: . ncompose(suc_rep;n;zero_rep) |
| | Thm* rep_num (hnum  hind) |
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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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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 |