| Who Cites habs sum? |
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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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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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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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tlambda | Def ( x:T. b(x))(x) == b(x) |
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bnot | Def  b == if b false else true fi |
| | Thm* b: .  b  |
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bequal | Def x = y ==  (x = y T) |
| | Thm* T:Type, x,y:T. (x = y)  |
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band | Def p q == if p q else false fi |
| | Thm* p,q: . (p q)  |
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arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | Thm* T:S. arb(T) T |
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prop_to_bool | Def  P == InjCase(lem(P) ; true ; false ) |
| | Thm* P:Prop. ( P)  |