Nuprl Lemma : es-causl_weakening_p-locl
∀es:EO. ∀p:E ─→ (E + Top). (causal-predecessor(es;p) ⇒ (∀e,e':E. (e p< e' ⇒ (e < e'))))
Proof
Definitions occuring in Statement :
es-p-locl: e p< e',
causal-predecessor: causal-predecessor(es;p),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
union: left + right
Lemmas :
es-p-locl_wf,
es-E_wf,
causal-predecessor_wf,
top_wf,
event_ordering_wf,
nat_plus_properties,
primrec-wf-nat-plus,
primrec1_lemma,
assert_wf,
can-apply_wf,
subtype_rel_dep_function,
subtype_rel_sum,
do-apply_wf,
and_wf,
equal_wf,
es-causl_wf,
p-graph_wf2,
p-fun-exp_wf,
decidable__le,
false_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_wf,
can-apply-fun-exp,
assert_elim,
subtype_base_sq,
bool_wf,
bool_subtype_base,
le-add-cancel2,
assert_functionality_wrt_uiff,
squash_wf,
true_wf,
p-fun-exp-one,
p-fun-exp-add,
le_weakening2,
iff_weakening_equal,
bool_cases,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
es-causl_transitivity2,
es-causle_weakening,
primrec_wf,
bool_cases_sqequal,
assert-bnot,
all_wf,
int_seg_wf,
nat_plus_wf,
nat_plus_subtype_nat
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top). (causal-predecessor(es;p) {}\mRightarrow{} (\mforall{}e,e':E. (e p< e' {}\mRightarrow{} (e < e'))))
Date html generated:
2015_07_17-AM-09_08_02
Last ObjectModification:
2015_02_04-PM-06_28_12
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