Nuprl Lemma : es-pplus-alle-between2
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[Q:{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ]. ([e1,e2]~([a,b].∀e∈[a,b].Q[e])+ ⇐⇒ e1 ≤loc e2 ∧ ∀e∈[e1,e2].Q[e])
Proof
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
alle-between2: ∀e∈[e1,e2].P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-le_wf,
es-locl-first,
decidable__lt,
false_wf,
less-iff-le,
subtract_wf,
condition-implies-le,
add-associates,
minus-add,
minus-one-mul,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel2,
lelt_wf,
es-E_wf,
Id_wf,
es-loc_wf,
decidable__le,
not-le-2,
sq_stable__le,
zero-add,
add-zero,
le-add-cancel,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
int_seg_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
map_nil_lemma,
reduce_nil_lemma,
list_ind_nil_lemma,
es-interval_wf,
squash_wf,
true_wf,
event_ordering_wf,
es-increasing-sequence,
subtype_rel_dep_function,
es-interval-partition,
minus-minus,
subtract-is-less,
es-le-loc,
not-equal-2,
es-causl_wf,
equal_wf,
list_wf,
append_wf,
le_wf,
nat_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
not-ge-2,
le_antisymmetry_iff,
list_subtype_base,
set_subtype_base,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
from-upto-nil,
cons_wf,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
map_cons_lemma,
reduce_cons_lemma,
append-nil,
es-pred_wf,
less_than_transitivity2,
le_weakening,
subtype_rel_list,
top_wf,
iff_weakening_equal,
upto_decomp1,
map_append_sq,
concat_append,
concat-cons,
concat-nil,
le-add-cancel-alt,
le_weakening2,
and_wf,
not_assert_elim,
trivial-int-eq1,
es-le-pred,
member-es-interval,
l_member_wf,
member_append,
concat_wf,
map_wf,
upto_wf,
member-concat,
member_map
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
([e1,e2]\msim{}([a,b].\mforall{}e\mmember{}[a,b].Q[e])+ \mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} \mforall{}e\mmember{}[e1,e2].Q[e])
Date html generated:
2015_07_17-AM-08_55_11
Last ObjectModification:
2015_02_04-PM-06_30_00
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