Nuprl Lemma : es-is-interface-filter
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A)]. ∀[P:A ⟶ 𝔹]. ∀[e:E].
uiff(↑e ∈b X|a.P[a];{(↑e ∈b X) ∧ (↑P[X(e)])})
Proof
Definitions occuring in Statement :
es-interface-filter: X|a.P[a],
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],
guard: {T},
so_apply: x[s],
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
guard: {T},
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
prop: ℙ,
top: Top,
rev_implies: P ⇐ Q,
eclass-val: X(e),
in-eclass: e ∈b X,
es-interface-filter: X|a.P[a],
eclass: EClass(A[eo; e]),
eclass-compose1: f o X,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
nat: ℕ,
ifthenelse: if b then t else f fi ,
assert: ↑b,
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,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
eq_int: (i =z j),
single-bag: {x},
bag-filter: [x∈b|p[x]],
bag-size: #(bs),
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} X|a.P[a];\{(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}P[X(e)])\})
Date html generated:
2016_05_16-PM-10_51_46
Last ObjectModification:
2016_01_17-PM-07_21_12
Theory : event-ordering
Home
Index