Nuprl Lemma : global-order-pairwise-compat-msg-and-classrel
∀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. ∀[e:E]. ∀[v:Interface]. (v ∈ X(e) ⇐⇒ v ∈ X(g e))))))))
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),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
es-E: E,
Id: Id,
name: Name,
pairwise: (∀x,y∈L. P[x; y]),
l_all: (∀x∈L.P[x]),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
l_all: (∀x∈L.P[x]),
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
label: ...$L... t
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. \mforall{}[e:E]. \mforall{}[v:Interface]. (v \mmember{} X(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} X(g e))))))))
Date html generated:
2016_05_17-AM-09_00_37
Last ObjectModification:
2016_01_17-PM-08_32_39
Theory : messages
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