Nuprl Lemma : es-filter-image-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(Top)]. ∀[e:E]. f[X](e) ~ only(f X(e)) supposing ↑e ∈b X
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t,
bag-only: only(bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eclass-val: X(e),
es-filter-image: f[X],
in-eclass: e ∈b X,
eclass-compose1: f o X,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
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,
nat: ℕ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
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].
f[X](e) \msim{} only(f X(e)) supposing \muparrow{}e \mmember{}\msubb{} X
Date html generated:
2016_05_16-PM-10_28_07
Last ObjectModification:
2015_12_29-AM-11_06_25
Theory : event-ordering
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