Nuprl Lemma : es-local-pred-iff-es-p-local-pred
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e,e':E.
uiff((last(λe'.0 <z #(X es e')) e) = (inl e') ∈ (E + Top);es-p-local-pred(es;λe'.inhabited-classrel(es;T;X;e')) e
e')
Proof
Definitions occuring in Statement :
es-local-pred: last(P),
inhabited-classrel: inhabited-classrel(eo;T;X;e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-local-pred: es-p-local-pred(es;P),
es-E: E,
lt_int: i <z j,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
apply: f a,
lambda: λx.A[x],
inl: inl x,
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-size: #(bs)
Lemmas :
equal_wf,
top_wf,
es-local-pred_wf,
lt_int_wf,
bag-size_wf,
subtype_rel_sum,
sq_exists_wf,
es-locl_wf,
assert_wf,
nat_wf,
all_wf,
not_wf,
or_wf,
es-p-local-pred_wf,
inhabited-classrel_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
es-causl-swellfnd,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
int_seg_subtype-nat,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
es-first_wf2,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
bfalse_wf,
and_wf,
isl_wf,
btrue_wf,
btrue_neq_bfalse,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
bnot_wf,
assert_of_lt_int,
iff_transitivity,
iff_weakening_uiff,
es-pred-locl,
squash_wf,
true_wf,
event_ordering_wf,
iff_weakening_equal,
bag-size-bag-member,
es-pred_property,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening_eq,
es-locl_irreflexivity,
es-causl_transitivity2,
es-causle_weakening,
es-causl_irreflexivity,
es-le_weakening,
sq_stable_from_decidable,
decidable__es-locl,
bag-member-size,
bag_wf,
nat_properties,
ge_wf,
not-ge-2,
bool_cases_sqequal,
assert-bnot,
es-locl-first,
assert_elim,
es-loc-pred
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e,e':E.
uiff((last(\mlambda{}e'.0 <z \#(X es e')) e)
= (inl e');es-p-local-pred(es;\mlambda{}e'.inhabited-classrel(es;T;X;e')) e e')
Date html generated:
2015_07_22-PM-00_14_52
Last ObjectModification:
2015_02_04-PM-04_41_11
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