Nuprl Lemma : lg-search-property
∀[T:Type]. ∀G:LabeledGraph(T). ∀P:T ─→ 𝔹. (↑isl(lg-search(G;x.P[x])) ⇐⇒ lg-exists(G;x.↑P[x]))
Proof
Definitions occuring in Statement :
lg-search: lg-search(G;x.P[x]),
lg-exists: lg-exists(G;x.P[x]),
labeled-graph: LabeledGraph(T),
assert: ↑b,
isl: isl(x),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
search_property,
lg-size_wf,
lg-label2_wf,
int_seg_wf,
nat_wf,
eq_int_wf,
search_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
false_wf,
less_than_transitivity1,
le_weakening,
less_than_irreflexivity,
exists_wf,
assert_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
true_wf
Latex:
\mforall{}[T:Type]. \mforall{}G:LabeledGraph(T). \mforall{}P:T {}\mrightarrow{} \mBbbB{}. (\muparrow{}isl(lg-search(G;x.P[x])) \mLeftarrow{}{}\mRightarrow{} lg-exists(G;x.\muparrow{}P[x]))
Date html generated:
2015_07_23-AM-11_04_53
Last ObjectModification:
2015_01_28-PM-11_34_45
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