Nuprl Lemma : local-class-single-valued-class-except
∀[f:Name ⟶ Type]. ∀[hdrs:Name List]. ∀[X:EClass(Interface)].
  (single-valued-class-except{i:l}(f;hdrs;X) 
⇒ (∀P:LocalClass(X). ∀a:Id.  hdf-single-valued-except(f;hdrs;P a)))
Proof
Definitions occuring in Statement : 
single-valued-class-except: single-valued-class-except{i:l}(f;hdrs;X)
, 
hdf-single-valued-except: hdf-single-valued-except(f;hdrs;X)
, 
msg-interface: Interface
, 
Message: Message(f)
, 
local-class: LocalClass(X)
, 
eclass: EClass(A[eo; e])
, 
Id: Id
, 
name: Name
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
apply: f a
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
label: ...$L... t
, 
hdf-single-valued-except: hdf-single-valued-except(f;hdrs;X)
, 
hdf-invariant: hdf-invariant(A;b.Q[b];X)
, 
local-class: LocalClass(X)
, 
sq_exists: ∃x:{A| B[x]}
, 
subtype_rel: A ⊆r B
, 
ext-eq: A ≡ B
, 
and: P ∧ Q
, 
hdf-run: hdf-run(P)
, 
top: Top
, 
unit: Unit
, 
it: ⋅
, 
hdf-halt: hdf-halt()
, 
true: True
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
nat_plus: ℕ+
, 
less_than: a < b
, 
squash: ↓T
, 
less_than': less_than'(a;b)
, 
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+
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
ge: i ≥ j 
, 
le: A ≤ B
, 
single-valued-class-except: single-valued-class-except{i:l}(f;hdrs;X)
, 
msg-interface: Interface
, 
pi2: snd(t)
, 
assert: ↑b
, 
ifthenelse: if b then t else f fi 
, 
btrue: tt
, 
sq_type: SQType(T)
, 
bool: 𝔹
, 
bfalse: ff
, 
bnot: ¬bb
, 
nat: ℕ
, 
select: L[n]
, 
cons: [a / b]
Latex:
\mforall{}[f:Name  {}\mrightarrow{}  Type].  \mforall{}[hdrs:Name  List].  \mforall{}[X:EClass(Interface)].
    (single-valued-class-except\{i:l\}(f;hdrs;X)
    {}\mRightarrow{}  (\mforall{}P:LocalClass(X).  \mforall{}a:Id.    hdf-single-valued-except(f;hdrs;P  a)))
Date html generated:
2016_05_17-AM-09_03_04
Last ObjectModification:
2016_01_17-PM-08_34_26
Theory : messages
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