Nuprl Lemma : until-class-simple-comb
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(Top)].
((X until Y) = λxs,ys.if bag-null(ys) then xs else {} fi |X;Prior(Y)| ∈ EClass(A))
Proof
Definitions occuring in Statement :
simple-comb2: λx,y.F[x; y]|X;Y|,
primed-class: Prior(X),
until-class: (X until Y),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
empty-bag: {}
Lemmas :
class-pred-cases,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bag_wf,
eqtt_to_assert,
assert-bag-null,
no-classrel-iff-empty,
primed-class_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
empty-bag_wf,
all_wf,
classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
primed-classrel,
es-locl_wf,
alle-lt_wf,
Id_wf,
es-loc_wf,
es-le_wf
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(Top)].
((X until Y) = \mlambda{}xs,ys.if bag-null(ys) then xs else \{\} fi |X;Prior(Y)|)
Date html generated:
2015_07_21-PM-03_19_24
Last ObjectModification:
2015_01_27-PM-07_22_48
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