Nuprl Lemma : base-process-class-program_wf
∀[f:Name ⟶ Type]. ∀[Info,T:Type]. ∀[loc:Id]. ∀[hdr:Name].
∀[X:EClass(T)]. ∀[P:LocalClass(X)].
(base-process-class-program(P;loc;hdr) ∈ LocalClass(base-process-class(X;loc;hdr)))
supposing hdr encodes Id × Info
Proof
Definitions occuring in Statement :
base-process-class-program: base-process-class-program(X;loc;hdr),
base-process-class: base-process-class(X;loc;hdr),
encodes-msg-type: hdr encodes T,
Message: Message(f),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
name: Name,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
top: Top,
base-process-class: base-process-class(X;loc;hdr),
class-ap: X(e),
encodes-msg-type: hdr encodes T,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
base-process-inputs: base-process-inputs(loc;hdr;es;e),
es-le-before: ≤loc(e),
mapfilter: mapfilter(f;P;L),
not: ¬A,
let: let,
msg-type: msg-type(msg;f),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
listp: A List+,
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
le: A ≤ B,
nat: ℕ
Latex:
\mforall{}[f:Name {}\mrightarrow{} Type]. \mforall{}[Info,T:Type]. \mforall{}[loc:Id]. \mforall{}[hdr:Name].
\mforall{}[X:EClass(T)]. \mforall{}[P:LocalClass(X)].
(base-process-class-program(P;loc;hdr) \mmember{} LocalClass(base-process-class(X;loc;hdr)))
supposing hdr encodes Id \mtimes{} Info
Date html generated:
2016_05_17-AM-09_08_32
Last ObjectModification:
2016_01_17-PM-09_14_33
Theory : local!classes
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