Nuprl Lemma : interface-predecessors-filter-image
∀[Info,A,B:Type]. ∀[f:A ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[e:E].
(≤(f[X])(e) ~ filter(λe.(#(f X(e)) =z 1);≤(X)(e)))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-filter-image: f[X],
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
filter: filter(P;l),
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs),
bag: bag(T)
Lemmas :
filter-filter,
filter-sq,
Id_wf,
es-loc_wf,
es-le-before_wf,
l_member_wf,
set_wf,
in-eclass_wf,
es-filter-image_wf,
top_wf,
subtype_rel_dep_function,
bag_wf,
subtype_rel_bag,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
bool_wf,
eqtt_to_assert,
eq_int_wf,
bag-size_wf,
eclass-val_wf,
nat_wf,
is-filter-image-sq,
assert_wf,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(\mleq{}(f[X])(e) \msim{} filter(\mlambda{}e.(\#(f X(e)) =\msubz{} 1);\mleq{}(X)(e)))
Date html generated:
2015_07_21-PM-03_39_24
Last ObjectModification:
2015_01_27-PM-06_29_33
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