Nuprl Lemma : CLK_mk_reply_wf
∀[MsgType:ValueAllType]. ∀[reply:Id ⟶ MsgType ⟶ (MsgType × Id)]. ∀[f:CLK_headers_type{i:l}(MsgType)].
(CLK_mk_reply(MsgType;reply;f) ∈ Id ⟶ (MsgType × ℤ) ⟶ ℤ ⟶ bag(Interface))
Proof
Definitions occuring in Statement :
CLK_mk_reply: CLK_mk_reply(MsgType;reply;f),
CLK_headers_type: CLK_headers_type{i:l}(MsgType),
msg-interface: Interface,
Id: Id,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
bag: bag(T)
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,
CLK_headers: CLK_headers(),
rev_implies: P ⇐ Q,
or: P ∨ Q,
uimplies: b supposing a,
guard: {T},
CLK_headers_fun: CLK_headers_fun(MsgType),
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
list_ind: list_ind,
cons: [a / b],
band: p ∧b q,
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
btrue: tt,
nil: [],
it: ⋅,
null: null(as),
CLK_mk_reply: CLK_mk_reply(MsgType;reply;f)
Latex:
\mforall{}[MsgType:ValueAllType]. \mforall{}[reply:Id {}\mrightarrow{} MsgType {}\mrightarrow{} (MsgType \mtimes{} Id)].
\mforall{}[f:CLK\_headers\_type\{i:l\}(MsgType)].
(CLK\_mk\_reply(MsgType;reply;f) \mmember{} Id {}\mrightarrow{} (MsgType \mtimes{} \mBbbZ{}) {}\mrightarrow{} \mBbbZ{} {}\mrightarrow{} bag(Interface))
Date html generated:
2016_05_17-PM-02_44_53
Last ObjectModification:
2015_12_29-PM-10_18_33
Theory : lamport!s!clocks
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