Nuprl Lemma : global-class-iff-bounded-local-class
∀[Info:Type]. ∀[A:{A:Type| valueall-type(A)} ]. ∀[X:EClass(A)].
(GlobalClass(Info;A;X) ⇐⇒ LocalClass(X) ∧ LocBounded(A;X))
Proof
Definitions occuring in Statement :
global-class: GlobalClass(Info;A;X),
local-class: LocalClass(X),
loc-bounded-class: LocBounded(T;X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
local-class: LocalClass(X),
global-class: GlobalClass(Info;A;X),
sq_exists: ∃x:{A| B[x]},
all: ∀x:A. B[x],
pi1: fst(t),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
pi2: snd(t),
sq_stable: SqStable(P),
squash: ↓T,
true: True,
guard: {T},
class-ap: X(e),
hdf-parallel-bag: hdf-parallel-bag(Xs),
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
compose: f o g,
rev_uimplies: rev_uimplies(P;Q),
bag-mapfilter: bag-mapfilter(f;P;bs),
cand: A c∧ B,
has-value: (a)↓,
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a),
bag-combine: ⋃x∈bs.f[x],
not: ¬A,
loc-bounded-class: LocBounded(T;X),
class-loc-bound: class-loc-bound{i:l}(Info;T;X;L),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
eclass: EClass(A[eo; e]),
decidable: Dec(P),
nat: ℕ,
single-bag: {x},
le: A ≤ B,
eq_id: a = b,
satisfiable_int_formula: satisfiable_int_formula(fmla),
deq: EqDecider(T)
Latex:
\mforall{}[Info:Type]. \mforall{}[A:\{A:Type| valueall-type(A)\} ]. \mforall{}[X:EClass(A)].
(GlobalClass(Info;A;X) \mLeftarrow{}{}\mRightarrow{} LocalClass(X) \mwedge{} LocBounded(A;X))
Date html generated:
2016_05_16-PM-02_07_27
Last ObjectModification:
2016_01_17-PM-07_50_55
Theory : event-ordering
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