Nuprl Lemma : hdf-until-ap-fst
∀[A,B,C:Type]. ∀[X:hdataflow(A;B)]. ∀[Y:hdataflow(A;C)]. ∀[a:A].
((fst(hdf-until(X;Y)(a)))
= if bag-null(snd(Y(a))) then hdf-until(fst(X(a));fst(Y(a))) else hdf-halt() fi
∈ hdataflow(A;B))
Proof
Definitions occuring in Statement :
hdf-until: hdf-until(X;Y),
hdf-halt: hdf-halt(),
hdf-ap: X(a),
hdataflow: hdataflow(A;B),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
pi1: fst(t),
pi2: snd(t),
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs)
Lemmas :
hdataflow_wf,
bool_wf,
eqtt_to_assert,
assert-bag-null,
hdf-until_wf,
hdf-ap_wf,
bag_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
hdf-halt_wf,
pi1_wf_top,
squash_wf,
true_wf,
top_wf,
hdf-until-ap,
subtype_rel_product,
subtype_top,
iff_weakening_equal
\mforall{}[A,B,C:Type]. \mforall{}[X:hdataflow(A;B)]. \mforall{}[Y:hdataflow(A;C)]. \mforall{}[a:A].
((fst(hdf-until(X;Y)(a)))
= if bag-null(snd(Y(a))) then hdf-until(fst(X(a));fst(Y(a))) else hdf-halt() fi )
Date html generated:
2015_07_17-AM-08_06_09
Last ObjectModification:
2015_02_03-PM-09_46_31
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