Nuprl Lemma : primed-class-opt-exists
∀[Info,B:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(B)]. ∀[init:Id ─→ bag(B)]. ∀[e:E].
((↓∃x:B. x ↓∈ init loc(e)) ⇒ (↓∃b:B. b ∈ Prior(X)?init(e)))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
squash_wf,
exists_wf,
bag-member_wf,
es-loc_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,
primed-class-opt-cases,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-first_wf2,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
lt_int_wf,
bag-size_wf,
es-pred_wf,
bag-size-bag-member,
le_int_wf,
es-pred-locl,
es-causl_weakening,
true_wf,
bag_wf,
es-pred-loc-base,
iff_weakening_equal,
Id_wf,
eclass_wf,
event-ordering+_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
assert_of_lt_int,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
primed-class-opt_wf
Latex:
\mforall{}[Info,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[e:E].
((\mdownarrow{}\mexists{}x:B. x \mdownarrow{}\mmember{} init loc(e)) {}\mRightarrow{} (\mdownarrow{}\mexists{}b:B. b \mmember{} Prior(X)?init(e)))
Date html generated:
2015_07_21-PM-03_18_21
Last ObjectModification:
2015_02_04-PM-06_17_07
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