Nuprl Lemma : decidable__existse-before
∀es:EO. ∀e':E. ∀[P:{e:E| loc(e) = loc(e') ∈ Id} ─→ ℙ]. (∀e@loc(e').Dec(P[e]) ⇒ Dec(∃e<e'.P[e]))
Proof
Definitions occuring in Statement :
existse-before: ∃e<e'.P[e],
alle-at: ∀e@i.P[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],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
event_ordering_wf,
es-locl-wellfnd,
event_system-level-subtype,
uall_wf,
es-E_wf,
Id_wf,
es-loc_wf,
alle-at_wf,
decidable_wf,
existse-before_wf,
all_wf,
es-locl_wf,
decidable_functionality,
not_wf,
assert_wf,
es-first_wf2,
or_wf,
es-pred-loc-base,
iff_weakening_equal,
es-pred_wf,
existse-before-iff,
bool_wf,
eqtt_to_assert,
decidable__cand,
true_wf,
decidable__not,
decidable__true,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
decidable__false,
decidable__or,
es-loc-pred,
es-pred-locl,
subtype_rel_sets
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e@loc(e').Dec(P[e]) {}\mRightarrow{} Dec(\mexists{}e<e'.P[e]))
Date html generated:
2015_07_17-AM-08_46_00
Last ObjectModification:
2015_02_04-PM-05_55_52
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