Nuprl Lemma : assert-is-filter-image
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(Top)]. ∀[e:E].
(↑e ∈b f[X] ~ if e ∈b X then ↑(#(f X(e)) =z 1) else False fi )
Proof
Definitions occuring in Statement :
es-filter-image: f[X],
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
false: False,
apply: f a,
natural_number: $n,
universe: Type,
sqequal: s ~ t,
bag-size: #(bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Top]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\muparrow{}e \mmember{}\msubb{} f[X] \msim{} if e \mmember{}\msubb{} X then \muparrow{}(\#(f X(e)) =\msubz{} 1) else False fi )
Date html generated:
2016_05_16-PM-10_27_25
Last ObjectModification:
2015_12_29-AM-11_05_28
Theory : event-ordering
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