Nuprl Lemma : is-mapfilter-class
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[f:Top]. ∀[X:EClass(A)]. ∀[e:E].
uiff(↑e ∈b (f[v] where v from X such that P[v]);(↑e ∈b X) ∧ (↑P[X(e)]))
Proof
Definitions occuring in Statement :
mapfilter-class: (f[v] where v from X such that P[v]),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
in-eclass: e ∈b X,
mapfilter-class: (f[v] where v from X such that P[v]),
es-filter-image: f[X],
eclass-val: X(e),
eclass-compose1: f o X,
member: t ∈ T,
uall: ∀[x:A]. B[x],
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,
ifthenelse: if b then t else f fi ,
assert: ↑b,
so_apply: x[s],
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
eq_int: (i =z j),
true: True,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:Top]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v]);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[X(e)]))
Date html generated:
2016_05_16-PM-10_29_13
Last ObjectModification:
2016_01_17-PM-07_25_13
Theory : event-ordering
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