Nuprl Lemma : firstn-le-before
∀[the_es:EO]. ∀[e:E]. ∀[n:ℕ]. firstn(n + 1;≤loc(e)) ~ ≤loc(before(e)[n]) supposing n < ||before(e)||
Proof
Definitions occuring in Statement :
es-le-before: ≤loc(e),
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],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Lemmas :
firstn-before,
less_than_wf,
length_wf,
es-E_wf,
es-before_wf,
nat_wf,
event_ordering_wf,
firstn_append,
subtype_rel_list,
top_wf,
cons_wf,
nil_wf,
decidable__le,
false_wf,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
less-iff-le,
le-add-cancel2,
lelt_wf,
firstn_decomp,
le_wf,
trivial-int-eq1
\mforall{}[the$_{es}$:EO]. \mforall{}[e:E]. \mforall{}[n:\mBbbN{}]. firstn(n + 1;\mleq{}loc(e)) \msim{} \mleq{}loc(before(e)[n]) su\000Cpposing n < ||before(e)||
Date html generated:
2015_07_17-AM-08_43_34
Last ObjectModification:
2015_01_27-PM-02_29_58
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