Nuprl Lemma : global-order-pairwise-compat-squash-invariant
∀[Info:Type]. ∀[P:Id ⟶ Info List+ ⟶ ℙ]. ∀[R:Id ⟶ Id ⟶ Info List+ ⟶ Info List+ ⟶ ℙ].
∀LL:(Id × Info) List List
((∀L1,L2∈LL. L1 || L2)
⇒ (∀L∈LL.squash-causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) global-eo(L))
⇒ (∃G:(Id × Info) List
((squash-causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) global-eo(G))
∧ (∀L∈LL.∃f:E ⟶ E. es-local-embedding(Info;global-eo(L);global-eo(G);f)))))
Proof
Definitions occuring in Statement :
global-order-compat: L1 || L2,
global-eo: global-eo(L),
squash-causal-invariant: squash-causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
es-E: E,
Id: Id,
pairwise: (∀x,y∈L. P[x; y]),
l_all: (∀x∈L.P[x]),
listp: A List+,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
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 :
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],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
list: T List,
squash-causal-invariant: squash-causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
top: Top,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
squash: ↓T,
global-order-compat: L1 || L2,
compat: l1 || l2,
or: P ∨ Q,
pi1: fst(t),
iff: P ⇐⇒ Q,
l_all: (∀x∈L.P[x]),
rev_implies: P ⇐ Q,
decidable: Dec(P),
less_than: a < b
Latex:
\mforall{}[Info:Type]. \mforall{}[P:Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}].
\mforall{}LL:(Id \mtimes{} Info) List List
((\mforall{}L1,L2\mmember{}LL. L1 || L2)
{}\mRightarrow{} (\mforall{}L\mmember{}LL.squash-causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) global-eo(L))
{}\mRightarrow{} (\mexists{}G:(Id \mtimes{} Info) List
((squash-causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) global-eo(G))
\mwedge{} (\mforall{}L\mmember{}LL.\mexists{}f:E {}\mrightarrow{} E. es-local-embedding(Info;global-eo(L);global-eo(G);f)))))
Date html generated:
2016_05_17-AM-08_39_01
Last ObjectModification:
2016_01_17-PM-02_31_56
Theory : event-ordering
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