Nuprl Lemma : mapfilter-class-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[P:A ⟶ 𝔹]. ∀[f:A ⟶ B]. ∀[X:EClass(A)]. ∀[e:E].
(f[v] where v from X such that P[v])(e) ~ f[X(e)] supposing ↑e ∈b (f[v] where v from X such that P[v])
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,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
mapfilter-class: (f[v] where v from X such that P[v]),
in-eclass: e ∈b X,
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 ,
top: Top,
eq_int: (i =z j),
assert: ↑b,
prop: ℙ,
bfalse: ff,
false: False,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[e:E].
(f[v] where v from X such that P[v])(e) \msim{} f[X(e)]
supposing \muparrow{}e \mmember{}\msubb{} (f[v] where v from X such that P[v])
Date html generated:
2016_05_16-PM-10_29_28
Last ObjectModification:
2016_01_17-PM-07_23_10
Theory : event-ordering
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