Nuprl Lemma : es-pstar-q-trivial
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[p,q:{e:E| loc(e) = loc(e1) ∈ Id} ─→ {e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ].
(e1 ≤loc e2 ⇒ q[e1;e2] ⇒ [e1;e2]~([a,b].p[a;b])*[a,b].q[a;b])
Proof
Definitions occuring in Statement :
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
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[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
less_than_wf,
es-loc_wf,
Id_wf,
int_seg_wf,
less_than_transitivity1,
less_than_irreflexivity,
es-E_wf,
false_wf,
lelt_wf,
es-le_wf,
subtract_wf,
all_wf,
es-locl_wf,
less-iff-le,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
add-associates,
add-swap,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
sq_stable__le,
exists_wf,
decidable__le,
not-le-2,
minus-minus,
add-commutes,
subtract-is-less,
decidable__lt,
le-add-cancel2,
set_wf,
es-pred-loc-base,
iff_weakening_equal,
es-pred_wf,
es-locl-first,
assert_elim,
btrue_neq_bfalse,
assert_wf,
es-first_wf2,
equal_wf
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[p,q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
(e1 \mleq{}loc e2 {}\mRightarrow{} q[e1;e2] {}\mRightarrow{} [e1;e2]\msim{}([a,b].p[a;b])*[a,b].q[a;b])
Date html generated:
2015_07_17-AM-08_53_39
Last ObjectModification:
2015_02_04-PM-05_56_03
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