Nuprl Lemma : primed-class-cases
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(Prior(X) es e ~ if first(e) then {}
if 0 <z #(X es pred(e)) then X es pred(e)
else Prior(X) es pred(e)
fi )
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs),
empty-bag: {}
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-E_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_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,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
lt_int_wf,
bag-size_wf,
top_wf,
es-pred_wf,
assert_of_lt_int,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(Prior(X) es e \msim{} if first(e) then \{\}
if 0 <z \#(X es pred(e)) then X es pred(e)
else Prior(X) es pred(e)
fi )
Date html generated:
2015_07_21-PM-03_18_30
Last ObjectModification:
2015_01_27-PM-07_19_45
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