Nuprl Lemma : global-order-compat-joint-embedding
∀[Info:Type]
∀L1,L2:(Id × Info) List.
(L1 || L2
⇒ (∃L:(Id × Info) List
((∃f:E ⟶ E. ∃g:E ⟶ E. es-weak-joint-embedding(Info;global-eo(L1);global-eo(L2);global-eo(L);f;g))
∧ (∀L':(Id × Info) List. (L1 || L' ⇒ L2 || L' ⇒ L || L')))))
Proof
Definitions occuring in Statement :
global-order-compat: L1 || L2,
global-eo: global-eo(L),
es-weak-joint-embedding: es-weak-joint-embedding(Info;eo1;eo2;eo;f;g),
es-E: E,
Id: Id,
list: T List,
uall: ∀[x:A]. B[x],
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
true: True,
es-weak-joint-embedding: es-weak-joint-embedding(Info;eo1;eo2;eo;f;g),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
Id: Id,
sq_type: SQType(T),
pi1: fst(t),
less_than': less_than'(a;b),
sq_stable: SqStable(P),
global-order-compat: L1 || L2
Latex:
\mforall{}[Info:Type]
\mforall{}L1,L2:(Id \mtimes{} Info) List.
(L1 || L2
{}\mRightarrow{} (\mexists{}L:(Id \mtimes{} Info) List
((\mexists{}f:E {}\mrightarrow{} E
\mexists{}g:E {}\mrightarrow{} E. es-weak-joint-embedding(Info;global-eo(L1);global-eo(L2);global-eo(L);f;g))
\mwedge{} (\mforall{}L':(Id \mtimes{} Info) List. (L1 || L' {}\mRightarrow{} L2 || L' {}\mRightarrow{} L || L')))))
Date html generated:
2016_05_17-AM-08_36_59
Last ObjectModification:
2016_01_17-PM-02_35_47
Theory : event-ordering
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