| Who Cites discrete equality? |
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discrete_equality | Def {T= } == {eq:(T T  )| x,y:T. (eq(x,y))  x = y } |
| | Thm* T:Type. {T= } Type |
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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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discrete | Def Discrete{T} == x,y:T. Dec(x = y) |
| | Thm* T:Type{i}. Discrete{T} Type{i'} |
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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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list_all | Def x L.P(x) == (letrec list_all L = (Case of L; nil True ; h.t P(h) & list_all(t)) ) (L) |
| | Thm* T:Type, P:(T Prop), L:T List. x L.P(x) Type |
| | Thm* T:Type, P:(T Type). x nil.P(x) Type |
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decidable | Def Dec(P) == P P |
| | Thm* A:Prop. Dec(A) Prop |
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iff | Def P  Q == (P  Q) & (P  Q) |
| | Thm* A,B:Prop. (A  B) 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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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |
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rev_implies | Def P  Q == Q  P |
| | Thm* A,B:Prop. (A  B) Prop |