Nuprl Lemma : firstn-before
∀[the_es:EO]. ∀[e:E]. ∀[n:ℕ]. firstn(n;before(e)) ~ before(before(e)[n]) supposing n < ||before(e)||
Proof
Definitions occuring in Statement :
es-before: before(e),
es-E: E,
event_ordering: EO,
select: L[n],
firstn: firstn(n;as),
length: ||as||,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
length_wf,
es-E_wf,
es-before_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,
bool_wf,
eqtt_to_assert,
length_of_nil_lemma,
list_ind_nil_lemma,
stuck-spread,
base_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
length-append,
length_of_cons_lemma,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
firstn_append,
subtype_rel_list,
top_wf,
cons_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
event_ordering_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
le_int_wf,
assert_of_lt_int,
lt_int_wf,
nil_wf,
select-append,
firstn_all,
int_subtype_base,
subtype_base_sq
\mforall{}[the$_{es}$:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. firstn(n;before(e)) \msim{} before(before(e)[n]) su\000Cpposing n < ||before(e)||
Date html generated:
2015_07_17-AM-08_43_27
Last ObjectModification:
2015_02_02-PM-06_42_28
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