Nuprl Lemma : C_Array-elem_vs_DVALp

store:C_STOREp(). ∀ctyp:C_TYPE(). ∀env:C_TYPE_env(). ∀dval:C_DVALUEp(). ∀n:ℤ.
  (C_STOREp-welltyped(env;store)
   (↑C_Array?(ctyp))
   (0 ≤ n)
   n < C_Array-length(ctyp)
   (↑(C_TYPE_vs_DVALp(env;ctyp) dval))
   (↑(C_TYPE_vs_DVALp(env;C_Array-elems(ctyp)) (DVp_Array-arr(dval) (DVp_Array-lower(dval) n)))))


Proof




Definitions occuring in Statement :  C_STOREp-welltyped: C_STOREp-welltyped(env;store) C_STOREp: C_STOREp() C_TYPE_vs_DVALp: C_TYPE_vs_DVALp(env;ctyp) DVp_Array-arr: DVp_Array-arr(v) DVp_Array-lower: DVp_Array-lower(v) C_DVALUEp: C_DVALUEp() C_TYPE_env: C_TYPE_env() C_Array-elems: C_Array-elems(v) C_Array-length: C_Array-length(v) C_Array?: C_Array?(v) C_TYPE: C_TYPE() assert: b less_than: a < b le: A ≤ B all: x:A. B[x] implies:  Q apply: a add: m natural_number: $n int:
Lemmas :  C_TYPE-ext eq_atom_wf bool_wf eqtt_to_assert assert_of_eq_atom subtype_base_sq atom_subtype_base unit_wf2 unit_subtype_base it_wf eqff_to_assert equal_wf bool_cases_sqequal bool_subtype_base assert-bnot neg_assert_of_eq_atom assert_wf C_TYPE_vs_DVALp_wf less_than_wf C_Array-length_wf nat_wf le_wf C_Array?_wf C_STOREp-welltyped_wf C_DVALUEp_wf C_TYPE_env_wf C_TYPE_wf C_STOREp_wf C_DVALUEp-ext eq_int_wf subtract_wf assert_of_eq_int bl-all_wf int_seg_wf upto_wf l_member_wf lelt_wf equal-wf-T-base int_subtype_base l_all_wf2 iff_transitivity iff_weakening_uiff assert_of_band assert-bl-all length_upto select-upto
\mforall{}store:C\_STOREp().  \mforall{}ctyp:C\_TYPE().  \mforall{}env:C\_TYPE\_env().  \mforall{}dval:C\_DVALUEp().  \mforall{}n:\mBbbZ{}.
    (C\_STOREp-welltyped(env;store)
    {}\mRightarrow{}  (\muparrow{}C\_Array?(ctyp))
    {}\mRightarrow{}  (0  \mleq{}  n)
    {}\mRightarrow{}  n  <  C\_Array-length(ctyp)
    {}\mRightarrow{}  (\muparrow{}(C\_TYPE\_vs\_DVALp(env;ctyp)  dval))
    {}\mRightarrow{}  (\muparrow{}(C\_TYPE\_vs\_DVALp(env;C\_Array-elems(ctyp)) 
                (DVp\_Array-arr(dval)  (DVp\_Array-lower(dval)  +  n)))))



Date html generated: 2015_07_17-AM-07_45_20
Last ObjectModification: 2015_01_27-AM-09_46_13

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