NuprlPrimitives Sections NuprlLIB Doc
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Def  == {i:| 0i }

is mentioned by

Thm* Y(f,x. if x=0 1 else xf(x-1) fi)  [sfa_doc_ycomb_factorial_typing]
Thm* (f,x. if x=0 1 else xf(x-1) fi)  (k:. (k)(k+1))[sfa_doc_factbody_polytyping]
Thm* (x.x) = (x.if x<0 0 ; x fi)  [sfa_doc_funeq_example1]
Thm* (n.n<0) = (n.false [sfa_doc_sqtype_ctr_example_part2]
Thm* x:y:yyx & x<(y+1)(y+1)[sfa_doc_nat_sqrt]
Thm* A:Type, a:Ae:(AA), i:i steps of e from a  A[sfa_doc_sequence_rel_wf]
Thm* (x.Case of x
Thm* (x.Canil  0
Thm* (x.Cau.v, rec:r  InjCase(if u<r inl(*) ; inr(.*) fi; arbu+1))
Thm* =
Thm* ext{sfa_doc_find_small_greater_bound}
Thm*  (k:x:(k List){y:(k+1)| y greater-bounds x })
[sfa_doc_find_small_greater_bound_extr_eq]
Thm* (k,xk)
Thm* =
Thm* ext{sfa_doc_find_greater_bound_stupidly}
Thm*  k:x:(k List){y:(k+1)| y greater-bounds x }
[sfa_doc_find_greater_bound_stupidly_extr_eq]
Thm* k:x:(k List){y:(k+1)| y greater-bounds x }[sfa_doc_find_greater_bound_stupidly]
Thm* k:x:(k List){y:(k+1)| y greater-bounds x }[sfa_doc_find_small_greater_bound]
Thm* f,g:().
Thm* (x:f zero beyond x) & (x:g zero beyond x)
Thm* 
Thm* (x:. (i.if i even f(i) else g(i) fi) zero beyond x)
[sfa_doc_alternate_zero_beyond]
Thm* a,b:. max(a;b [sfa_doc_max_int_wf]
Thm* x:f:(). f zero beyond x  Prop[sfa_doc_props_as_types_example1_wf]
Thm* P  Q  (x:. (x = 0  P) & (x  0  Q))[sfa_doc_or_dec]
Thm* f:(). 
Thm* (n:f(n) = 0)
Thm* 
Thm* (n:. if f(n)=0 False else C:Prop{1}. C fi)  Prop{1}
[sfa_doc_predicativity_sample8]
Thm* A:Type, P:(AProp), n:X:(A^n). ( u in XA^nP(u))  Prop[sfa_doc_ntuple_contains_wf]
Thm* n:n (A^n) = A(A^(n-1))[sfa_doc_ntuple_is_prod]
Thm* A:Type, n:. (A^n Type[sfa_doc_ntuple_wf]
Thm* x:{x:| (x rem 2) = 0 }. x!  [sfa_doc_factorial2_wf]
Thm* x:x [sfa_doc_factorial_wf]
Thm* k:. 0<k & (2  k)<1  2<k[sfa_doc_cand_example]
Thm* f:{f:()| x:f(x) }, i:i<mu(f f(i)[kleene_minimize_is_lb]
Thm* f:{f:()| x:f(x) }. f(mu(f))[kleene_minimize_is_fp]
Thm* mu  {f:()| x:f(x) }[kleene_minimize_wf]
Thm* f:{f:()| x:f(x) }. f(0)  (x.f(1+x))  {f:()| x:f(x) }[kleene_tail]
Def f zero beyond x == y:x<y  f(y) = 0  [sfa_doc_props_as_types_example1]
Def sfa_doc_oparm_sample{2:n}(A) == A[sfa_doc_oparm_sample2]
Def sfa_doc_oparm_sample{1:n}(A) == A[sfa_doc_oparm_sample1]
Def Induction for x:P(x) == P(0) & (x:P(x P(x+1))  (x:P(x))[sfa_doc_indscheme]
Def  u in XA^nP(u)
Def == n = 1   & P(X n2 & (X/a,restP(a ( u in restA^(n-1). P(u)))
Def (recursive)
[sfa_doc_ntuple_contains]

In prior sections: int 1 bool 1 int 2 list 1 sqequal 1

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NuprlPrimitives Sections NuprlLIB Doc