Nuprl Lemma : CLK_Reply-program_wf
∀[MsgType:ValueAllType]. ∀[reply:Id ⟶ MsgType ⟶ (MsgType × Id)]. ∀[f:CLK_headers_type{i:l}(MsgType)].
(CLK_Reply-program(MsgType;reply;f) ∈ LocalClass(CLK_Reply(MsgType;reply;f)))
Proof
Definitions occuring in Statement :
CLK_Reply-program: CLK_Reply-program(MsgType;reply;f),
CLK_Reply: CLK_Reply(MsgType;reply;f),
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
msg-interface: Interface,
Message: Message(f),
local-class: LocalClass(X),
Id: Id,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x]
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
l_all: (∀x∈L.P[x]),
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
listp: A List+,
name: Name,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
less_than: a < b,
squash: ↓T,
length: ||as||,
list_ind: list_ind,
CLK_headers: CLK_headers(),
cons: [a / b],
nil: [],
it: ⋅,
true: True,
select: L[n],
uimplies: b supposing a,
guard: {T},
rev_implies: P ⇐ Q,
CLK_headers_fun: CLK_headers_fun(MsgType),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
null: null(as),
CLK_Reply: CLK_Reply(MsgType;reply;f),
CLK_Reply-program: CLK_Reply-program(MsgType;reply;f),
exists: ∃x:A. B[x],
msg-interface: Interface
Latex:
\mforall{}[MsgType:ValueAllType]. \mforall{}[reply:Id {}\mrightarrow{} MsgType {}\mrightarrow{} (MsgType \mtimes{} Id)].
\mforall{}[f:CLK\_headers\_type\{i:l\}(MsgType)].
(CLK\_Reply-program(MsgType;reply;f) \mmember{} LocalClass(CLK\_Reply(MsgType;reply;f)))
Date html generated:
2016_05_17-PM-02_45_02
Last ObjectModification:
2016_01_18-AM-09_50_23
Theory : lamport!s!clocks
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