Nuprl Lemma : hdf-state-base

[f,C,F,s:Top].
  (hdf-state((λx,s. f[x;s]) hdf-base(a.if C[a] then [F[a]] else [] fi );[s]) 
  fix((λmk-hdf,s. (inl a.cbva_seq(λn.if C[a] then f[F[a];s] else fi ; λg.<mk-hdf (g x.x)), x.[x])>1))))) s\000C)


Proof




Definitions occuring in Statement :  hdf-state: hdf-state(X;bs) hdf-compose1: X hdf-base: hdf-base(m.F[m]) cons: [a b] nil: [] ifthenelse: if then else fi  uall: [x:A]. B[x] top: Top so_apply: x[s1;s2] so_apply: x[s] apply: a fix: fix(F) lambda: λx.A[x] pair: <a, b> inl: inl x natural_number: $n sqequal: t cbva_seq: cbva_seq(L; F; m)
Lemmas :  hdf-base-transformation1 hdf-compose1-transformation1-2 false_wf le_wf hdf-state-transformation2 primrec0_lemma primrec1_lemma map-ifthenelse map_cons_lemma map_nil_lemma nat_properties less_than_transitivity1 less_than_irreflexivity ge_wf less_than_wf base_wf fun_exp0_lemma strictness-apply bottom-sqle decidable__le subtract_wf not-ge-2 less-iff-le condition-implies-le minus-one-mul zero-add minus-add minus-minus add-associates add-swap add-commutes add_functionality_wrt_le add-zero le-add-cancel fun_exp_unroll_1 bag-combine-unit-left-top list_ind_cons_lemma list_ind_nil_lemma callbyvalueall-single cbv_sqle int_subtype_base evalall-sqequal null_cons_lemma has-valueall-single has-value_wf_base has-valueall_wf_base top_wf primrec-unroll callbyvalueall-ifthenelse
\mforall{}[f,C,F,s:Top].
    (hdf-state((\mlambda{}x,s.  f[x;s])  o  hdf-base(a.if  C[a]  then  [F[a]]  else  []  fi  );[s]) 
    \msim{}  fix((\mlambda{}mk-hdf,s.  (inl  (\mlambda{}a.cbva\_seq(\mlambda{}n.if  C[a]  then  f[F[a];s]  else  s  fi  ;  \mlambda{}g.<mk-hdf  (g  (\mlambda{}x.x))
                                                                                                                                                              ,  g  (\mlambda{}x.[x])
                                                                                                                                                              >  1))))) 
        s)



Date html generated: 2015_07_17-AM-08_15_31
Last ObjectModification: 2015_04_23-PM-11_31_52

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