Nuprl Lemma : single-valued-class-implies-hdf
∀[Info,A:Type].
∀X:EClass(A). ∀pr:LocalClass(X).
(single-valued-classrel-all{i:l}(Info;A;X) ⇒ (∀i:Id. hdf-single-valued(pr i;Info;A)))
Proof
Definitions occuring in Statement :
local-class: LocalClass(X),
single-valued-classrel-all: single-valued-classrel-all{i:l}(Info;T;X),
eclass: EClass(A[eo; e]),
hdf-single-valued: hdf-single-valued(X;A;B),
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
hdf-single-valued: hdf-single-valued(X;A;B),
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
member: t ∈ T,
subtype_rel: A ⊆r B,
ext-eq: A ≡ B,
and: P ∧ Q,
prop: ℙ,
hdf-run: hdf-run(P),
true: True,
unit: Unit,
it: ⋅,
hdf-halt: hdf-halt(),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
single-valued-bag: single-valued-bag(b;T),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
uimplies: b supposing a,
top: Top,
pi1: fst(t),
pi2: snd(t),
hdf-ap: X(a),
nat_plus: ℕ+,
less_than: a < b,
less_than': less_than'(a;b),
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
listp: A List+,
es-le-before: ≤loc(e),
ge: i ≥ j ,
Id: Id,
sq_type: SQType(T),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
class-ap: X(e)
Latex:
\mforall{}[Info,A:Type].
\mforall{}X:EClass(A). \mforall{}pr:LocalClass(X).
(single-valued-classrel-all\{i:l\}(Info;A;X) {}\mRightarrow{} (\mforall{}i:Id. hdf-single-valued(pr i;Info;A)))
Date html generated:
2016_05_17-AM-08_48_51
Last ObjectModification:
2016_01_17-PM-02_43_07
Theory : event-ordering
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