Nuprl Lemma : primed-class-equal
∀[Info,T:Type]. ∀[X,Y:EClass(T)]. ∀[es:EO+(Info)]. ∀[e:E].
(Prior(X) es e) = (Prior(Y) es e) ∈ bag(T) supposing ∀e':E. ((e' <loc e) ⇒ ((X es e') = (Y es e') ∈ bag(T)))
Proof
Definitions occuring in Statement :
primed-class: Prior(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
all_wf,
es-locl_wf,
bag_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,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
es-interface-subtype_rel2,
top_wf,
es-first_wf2,
bool_wf,
eqtt_to_assert,
empty-bag_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
ifthenelse_wf,
squash_wf,
true_wf,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening,
iff_weakening_equal,
lt_int_wf,
bag-size_wf,
assert_of_lt_int,
primed-class_wf,
primed-class-cases
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
(Prior(X) es e) = (Prior(Y) es e) supposing \mforall{}e':E. ((e' <loc e) {}\mRightarrow{} ((X es e') = (Y es e')))
Date html generated:
2015_07_21-PM-03_19_10
Last ObjectModification:
2015_02_04-PM-06_16_54
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