Nuprl Lemma : hdf-memory-base2-3

[F1,F2,f1,f2,s:Top]. ∀[hdr1,hdr2:Name].
  hdf-memory((λx,s. f1[x;s]) hdf-base(a.if name_eq(fst(a);hdr1) then [F1[a]] else [] fi || x,s. f2[x;s])
              hdf-base(a.if name_eq(fst(a);hdr2) then [F2[a]] else [] fi );[s]) 
  fix((λmk-hdf,s. (inl a.cbva_seq(λn.if name_eq(fst(a);hdr1) then f1[F1[a];s]
                                         if name_eq(fst(a);hdr2) then f2[F2[a];s]
                                         else s
                                         fi ; λg.<mk-hdf (g x.x)), [s]>1))))) 
    
  supposing ¬(hdr1 hdr2 ∈ Name)


Proof




Definitions occuring in Statement :  hdf-parallel: || Y hdf-memory: hdf-memory(X;bs) hdf-compose1: X hdf-base: hdf-base(m.F[m]) name_eq: name_eq(x;y) name: Name cons: [a b] nil: [] ifthenelse: if then else fi  uimplies: supposing a uall: [x:A]. B[x] top: Top so_apply: x[s1;s2] so_apply: x[s] pi1: fst(t) not: ¬A apply: a fix: fix(F) lambda: λx.A[x] pair: <a, b> inl: inl x natural_number: $n sqequal: t equal: t ∈ T cbva_seq: cbva_seq(L; F; m)
Lemmas :  hdf-base-transformation1 false_wf le_wf hdf-memory-transformation2 primrec1_lemma primrec0_lemma primrec-unroll 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 callbyvalueall-ifthenelse ifthenelse_sqle name_eq-is-inl callbyvalueall-single not-name_eq-implies-sq-bfalse equal_wf name_wf list_ind_cons_lemma list_ind_nil_lemma bag-combine-unit-left-top cbv_sqle int_subtype_base list_subtype_base atom_subtype_base evalall-sqequal null_cons_lemma has-valueall_wf_base exists_wf sqequal-wf-base not_wf top_wf hdf-compose1-transformation2 hdf-parallel-transformation2-1
\mforall{}[F1,F2,f1,f2,s:Top].  \mforall{}[hdr1,hdr2:Name].
    hdf-memory((\mlambda{}x,s.  f1[x;s])  o  hdf-base(a.if  name\_eq(fst(a);hdr1)  then  [F1[a]]  else  []  fi  )
                          ||  (\mlambda{}x,s.  f2[x;s])  o  hdf-base(a.if  name\_eq(fst(a);hdr2)  then  [F2[a]]  else  []  fi  );[s]) 
    \msim{}  fix((\mlambda{}mk-hdf,s.  (inl  (\mlambda{}a.cbva\_seq(\mlambda{}n.if  name\_eq(fst(a);hdr1)  then  f1[F1[a];s]
                                                                                  if  name\_eq(fst(a);hdr2)  then  f2[F2[a];s]
                                                                                  else  s
                                                                                  fi  ;  \mlambda{}g.<mk-hdf  (g  (\mlambda{}x.x)),  [s]>  1))))) 
        s 
    supposing  \mneg{}(hdr1  =  hdr2)



Date html generated: 2015_07_17-AM-08_16_31
Last ObjectModification: 2015_04_17-AM-03_02_12

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