Nuprl Lemma : global-order-pairwise-compat-msg-interface-constraint
∀f:Name ⟶ Type. ∀hdrs:Name List. ∀X:EClass(Interface).
(LocalClass(X)
⇒ (∀LL:(Id × Message(f)) List List
((∀L1,L2∈LL. L1 || L2)
⇒ (∀L∈LL.eo-msg-interface-constraint(global-eo(L);X;hdrs;f))
⇒ (∃G:(Id × Message(f)) List
(eo-msg-interface-constraint(global-eo(G);X;hdrs;f)
∧ (∀L∈LL.∃g:E ⟶ E. es-local-embedding(Message(f);global-eo(L);global-eo(G);g)))))))
Proof
Definitions occuring in Statement :
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
msg-interface: Interface,
Message: Message(f),
global-order-compat: L1 || L2,
global-eo: global-eo(L),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
es-E: E,
Id: Id,
name: Name,
pairwise: (∀x,y∈L. P[x; y]),
l_all: (∀x∈L.P[x]),
list: T List,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
label: ...$L... t,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
exists: ∃x:A. B[x],
listp: A List+,
uimplies: b supposing a,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
not: ¬A,
false: False,
cons: [a / b],
top: Top,
bfalse: ff,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
eo-msg-interface-constraint: eo-msg-interface-constraint(es;X;hdrs;f),
squash-causal-invariant: squash-causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2),
es-local-property: es-local-property(i,L.P[i; L];es;e),
es-le-before: ≤loc(e),
subtype_rel: A ⊆r B,
last: last(L),
subtract: n - m,
select: L[n],
es-header: header(e),
squash: ↓T,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_lambda: λ2x y.t[x; y],
rev_implies: P ⇐ Q,
cand: A c∧ B,
classrel: v ∈ X(e),
class-ap: X(e),
nat: ℕ,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
l_all: (∀x∈L.P[x]),
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
less_than: a < b
Latex:
\mforall{}f:Name {}\mrightarrow{} Type. \mforall{}hdrs:Name List. \mforall{}X:EClass(Interface).
(LocalClass(X)
{}\mRightarrow{} (\mforall{}LL:(Id \mtimes{} Message(f)) List List
((\mforall{}L1,L2\mmember{}LL. L1 || L2)
{}\mRightarrow{} (\mforall{}L\mmember{}LL.eo-msg-interface-constraint(global-eo(L);X;hdrs;f))
{}\mRightarrow{} (\mexists{}G:(Id \mtimes{} Message(f)) List
(eo-msg-interface-constraint(global-eo(G);X;hdrs;f)
\mwedge{} (\mforall{}L\mmember{}LL.\mexists{}g:E {}\mrightarrow{} E. es-local-embedding(Message(f);global-eo(L);global-eo(G);g)))))))
Date html generated:
2016_05_17-AM-09_00_32
Last ObjectModification:
2016_01_17-PM-08_35_08
Theory : messages
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