| Who Cites equivalence? |
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equivalence | Def {T } == {f:(T T  )| ( x:T. (f(x,x))) & ( x,y:T. (f(x,y))  (f(y,x))) & ( x,y,z:T. (f(x,y))  (f(y,z))  (f(x,z))) } |
| | Thm* T:Type{i}. {T } Type{i'} |
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assert | Def b == if b True else False fi |
| | Thm* b: . b Prop |
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ge | Def i j == j i |
| | Thm* i,j: . (i j) Prop |
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hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
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is_member | Def x( eq) L == (letrec is_member x eq L = (Case of L; nil false ; h.t if eq(x,h) true else is_member(x,eq,t) fi) ) (x,eq,L) |
| | Thm* T:Type, eq:(T T  ), u:T. u( eq) nil  |
| | Thm* T:Type, eq:(T T  ), x:T, L:T List. x( eq) L  |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l||  |
| | Thm* ||nil||  |
| | Thm* T:Type, L:T List. ||L||  |
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iff | Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) Prop |
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le | Def A B == B < A |
| | Thm* i,j: . (i j) Prop |
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letrec_body | Def = b == b |
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letrec_arg | Def x b(x) (x) == b(x) |
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letrec | Def (letrec f b(f)) == b((letrec f b(f)) ) (recursive) |
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rev_implies | Def P  Q == Q  P |
| | Thm* A,B:Prop. (A  B) Prop |
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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |