Nuprl Lemma : es-pplus-first-since
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[Q:{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ]
((∀e:{e:E| loc(e) = loc(e1) ∈ Id} . Dec(Q[e])) ⇒ ([e1,e2]~([a,b].b = first e ≥ a.Q[e])+ ⇐⇒ e1 ≤loc e2 ∧ Q[e2]))
Proof
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-first-since: e2 = first e ≥ e1.P[e],
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
int_seg_properties,
le_wf,
es-le-loc,
Id_wf,
es-loc_wf,
es-le_wf,
length_wf,
es-interval_wf,
equal_wf,
all_wf,
es-pplus_wf,
es-first-since_wf,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
lelt_wf,
es-E_wf,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
nat_wf,
decidable__existse-between1,
es-next,
es-pred-locl,
es-le_transitivity,
es-pred_wf,
es-le_weakening_eq,
es-locl_transitivity1,
es-interval-partition,
list_wf,
append_wf,
es-interval-non-zero,
length-append,
es-loc-pred,
and_wf,
es-pplus-partition,
member_wf,
es-pplus-trivial,
es-locl_wf,
length_wf_nat
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:\{e:E| loc(e) = loc(e1)\} . Dec(Q[e]))
{}\mRightarrow{} ([e1,e2]\msim{}([a,b].b = first e \mgeq{} a.Q[e])+ \mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} Q[e2]))
Date html generated:
2015_07_17-AM-08_55_21
Last ObjectModification:
2015_01_27-PM-01_05_25
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