Nuprl Lemma : tl-es-le-before
∀es:EO. ∀e,e':E. ((e' ∈ tl(≤loc(e))) ⇐⇒ e' ≤loc e ∧ (¬↑first(e')))
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-le: e ≤loc e' ,
es-first: first(e),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
tl: tl(l),
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
and: P ∧ Q
Lemmas :
es-pred_wf,
es-pred-locl,
es-causl_weakening,
es-le-before_wf,
list_wf,
es-E_wf,
Id_wf,
es-loc_wf,
set_wf,
list-cases,
product_subtype_list,
es-le-before-not-null,
null_wf3,
subtype_rel_list,
top_wf,
null_nil_lemma,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
l_member_wf,
nil_wf,
es-le_wf,
not_wf,
iff_wf,
reduce_tl_cons_lemma,
list_ind_cons_lemma,
member_append,
cons_wf,
member_singleton,
or_wf,
append_wf,
equal_wf,
es-locl_transitivity1,
es-le_weakening,
es-le-self,
and_wf,
assert_elim,
not_assert_elim,
es-le-pred
\mforall{}es:EO. \mforall{}e,e':E. ((e' \mmember{} tl(\mleq{}loc(e))) \mLeftarrow{}{}\mRightarrow{} e' \mleq{}loc e \mwedge{} (\mneg{}\muparrow{}first(e')))
Date html generated:
2015_07_17-AM-08_43_17
Last ObjectModification:
2015_01_27-PM-02_42_49
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