| Some definitions of interest. |
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habs_sum | Def abs_sum == f:  'a 'b  . @u:'a+'b. (rep_sum(u) = f   'a 'b  ) |
| | Thm* 'a,'b:S. abs_sum ((hbool  'a  'b  hbool)  hsum('a; 'b)) |
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his_sum_rep | Def is_sum_rep == f:  'a 'b  .  u:'a+'b. (f = (rep_sum(u))) |
| | Thm* 'a,'b:S. is_sum_rep ((hbool  'a  'b  hbool)  hbool) |
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hrep_sum | Def rep_sum
Def == u:'a+'b. InjCase(u
Def == u:'a+'b. InjCase; p. b: . x:'a. y:'b. (x = p) b
Def == u:'a+'b. InjCase; q. b: . x:'a. y:'b. (y = q)   b) |
| | Thm* 'a,'b:S. rep_sum (hsum('a; 'b)  hbool  'a  'b  hbool) |
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bequal | Def x = y ==  (x = y T) |
| | Thm* T:Type, x,y:T. (x = y)  |
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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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stype | Def S == {T:Type| x:T. True } |
| | Thm* S Type{2} |