| Some definitions of interest. |
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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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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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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 |