Nuprl Lemma : prior-val-as-latest-val
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e,p:E].
(((X)' es e) = ((X)- es p) ∈ bag(T)) supposing
((∀e'':E. ((e'' <loc e) ⇒ (p <loc e'') ⇒ (¬↑e'' ∈b X))) and
(p <loc e))
Proof
Definitions occuring in Statement :
es-latest-val: (X)-,
es-prior-val: (X)',
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
all_wf,
es-E_wf,
es-locl_wf,
not_wf,
assert_wf,
in-eclass_wf,
int_seg_wf,
es-interface-subtype_rel2,
top_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,
prior-val-pred,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
es-first_wf2,
es-pred_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
eqff_to_assert,
assert_of_bnot,
equal_wf,
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,
es-locl-iff,
es-pred-locl,
bool_wf,
single-bag_wf,
squash_wf,
true_wf,
eclass-val_wf,
subtype_top,
event-ordering+_cumulative2,
iff_weakening_equal,
assert_functionality_wrt_uiff,
es-prior-val_wf,
es-causl_weakening,
es-locl_transitivity2,
es-le_weakening
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[e,p:E].
(((X)' es e) = ((X)\msupminus{} es p)) supposing
((\mforall{}e'':E. ((e'' <loc e) {}\mRightarrow{} (p <loc e'') {}\mRightarrow{} (\mneg{}\muparrow{}e'' \mmember{}\msubb{} X))) and
(p <loc e))
Date html generated:
2015_07_21-PM-03_23_26
Last ObjectModification:
2015_02_04-PM-06_17_50
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