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)
Definitions unfolded in proof :
es-interface-predecessors: ≤(X)(e),
eclass-events: eclass-events(es;X;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
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:
2016_05_17-AM-07_04_44
Last ObjectModification:
2015_12_29-AM-00_13_11
Theory : event-ordering
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