Nuprl Lemma : hd-es-le-before-is-first
∀[es:EO]. ∀[e:E]. (first(hd(≤loc(e))) ~ tt)
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
es-first: first(e),
es-E: E,
event_ordering: EO,
hd: hd(l),
btrue: tt,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Lemmas :
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_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,
es-first_wf2,
eqtt_to_assert,
list_ind_nil_lemma,
reduce_hd_cons_lemma,
iff_imp_equal_bool,
btrue_wf,
assert_wf,
true_wf,
uiff_transitivity,
equal-wf-T-base,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-E_wf,
event_ordering_wf,
squash_wf,
es-le-before_wf,
list_wf,
Id_wf,
es-loc_wf,
set_wf,
list-cases,
product_subtype_list,
list_ind_cons_lemma,
null_wf3,
subtype_rel_list,
top_wf,
es-le-before-not-null,
null_nil_lemma,
btrue_neq_bfalse
\mforall{}[es:EO]. \mforall{}[e:E]. (first(hd(\mleq{}loc(e))) \msim{} tt)
Date html generated:
2015_07_17-AM-08_43_12
Last ObjectModification:
2015_01_27-PM-02_42_16
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