Nuprl Lemma : hd-es-le-before
∀es:EO. ∀e,fst:E. ((↑first(fst)) ⇒ fst ≤loc e ⇒ (hd(≤loc(e)) = fst ∈ 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,
hd: hd(l),
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
es-le_wf,
assert_wf,
es-first_wf2,
es-E_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,
bool_wf,
eqtt_to_assert,
list_ind_nil_lemma,
reduce_hd_cons_lemma,
assert_elim,
and_wf,
equal_wf,
ifthenelse_wf,
es-le-first,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
event_ordering_wf,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
es-le-pred,
not_assert_elim,
btrue_neq_bfalse,
es-le-before_wf,
list_wf,
Id_wf,
es-loc_wf,
set_wf,
list-cases,
product_subtype_list,
null_cons_lemma,
bfalse_wf,
append_is_nil,
es-before_wf2,
cons_wf,
null_wf3,
subtype_rel_list,
top_wf,
null_nil_lemma,
btrue_wf,
equal-wf-base-T,
list_ind_cons_lemma
\mforall{}es:EO. \mforall{}e,fst:E. ((\muparrow{}first(fst)) {}\mRightarrow{} fst \mleq{}loc e {}\mRightarrow{} (hd(\mleq{}loc(e)) = fst))
Date html generated:
2015_07_17-AM-08_43_09
Last ObjectModification:
2015_01_27-PM-02_40_58
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