Nuprl Lemma : joint-embedding-preserves-causal-invariant
∀[Info:Type]. ∀[R:Id ─→ Id ─→ Info List+ ─→ Info List+ ─→ ℙ]. ∀[P:Id ─→ Info List+ ─→ ℙ].
∀eo1,eo2,eo:EO+(Info). ∀f:E ─→ E. ∀g:E ─→ E.
(es-joint-embedding(Info;eo1;eo2;eo;f;g)
⇒ (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo1)
⇒ (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo2)
⇒ (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo))
Proof
Definitions occuring in Statement :
causal-invariant: causal-invariant(i,L.P[i; L];a,b,L1,L2.R[a; b; L1; L2]),
es-joint-embedding: es-joint-embedding(Info;eo1;eo2;eo;f;g),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
listp: A 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],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
causal-invariant_wf,
es-local-property_wf,
listp_wf,
Id_wf,
es-E_wf,
event-ordering+_subtype,
es-joint-embedding_wf,
event-ordering+_wf,
embedding-preserves-local-property,
es-causl_wf,
es-local-relation_wf,
and_wf,
equal_wf,
embedding-preserves-local-relation,
squash_wf,
true_wf
\mforall{}[Info:Type]. \mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}].
\mforall{}eo1,eo2,eo:EO+(Info). \mforall{}f:E {}\mrightarrow{} E. \mforall{}g:E {}\mrightarrow{} E.
(es-joint-embedding(Info;eo1;eo2;eo;f;g)
{}\mRightarrow{} (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo1)
{}\mRightarrow{} (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo2)
{}\mRightarrow{} (causal-invariant(i,L.P[i;L];a,b,L1,L2.R[a;b;L1;L2]) eo))
Date html generated:
2015_07_17-PM-00_13_12
Last ObjectModification:
2015_01_28-AM-00_07_17
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