Nuprl Lemma : local-class-only-headers
∀[f:Name ⟶ Type]. ∀[hdrs:Name List]. ∀[X:EClass(Interface)].
(class-only-headers{i:l}(f;hdrs;X) ⇒ (∀P:LocalClass(X). ∀a:Id. hdf-only-headers(f;hdrs;P a)))
Proof
Definitions occuring in Statement :
class-only-headers: class-only-headers{i:l}(f;hdrs;X),
hdf-only-headers: hdf-only-headers(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-only-headers: hdf-only-headers(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,
class-only-headers: class-only-headers{i:l}(f;hdrs;X),
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],
pi2: snd(t)
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[hdrs:Name List]. \mforall{}[X:EClass(Interface)].
(class-only-headers\{i:l\}(f;hdrs;X) {}\mRightarrow{} (\mforall{}P:LocalClass(X). \mforall{}a:Id. hdf-only-headers(f;hdrs;P a)))
Date html generated:
2016_05_17-AM-09_03_12
Last ObjectModification:
2016_01_17-PM-08_34_35
Theory : messages
Home
Index