Nuprl Lemma : embedding-preserves-local-relation
∀[Info:Type]. ∀[R:Id ─→ Id ─→ Info List+ ─→ Info List+ ─→ ℙ]. ∀[eo1:EO+(Info)].
∀eo2:EO+(Info). ∀f:E ─→ E.
(es-local-embedding(Info;eo1;eo2;f)
⇒ (∀[e1,e2:E].
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo1;e1;e2)
⇐⇒ es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo2;f e1;f e2))))
Proof
Definitions occuring in Statement :
es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
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],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_of_lt_int,
map-length,
length-append,
length_wf,
es-before_wf,
cons_wf,
nil_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_wf_nat,
length_cons,
assert_wf,
lt_int_wf,
es-local-relation_wf,
listp_wf,
Id_wf,
es-E_wf,
event-ordering+_subtype,
es-local-embedding_wf,
event-ordering+_wf
\mforall{}[Info:Type]. \mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[eo1:EO+(Info)].
\mforall{}eo2:EO+(Info). \mforall{}f:E {}\mrightarrow{} E.
(es-local-embedding(Info;eo1;eo2;f)
{}\mRightarrow{} (\mforall{}[e1,e2:E].
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo1;e1;e2)
\mLeftarrow{}{}\mRightarrow{} es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo2;f e1;f e2))))
Date html generated:
2015_07_17-PM-00_12_19
Last ObjectModification:
2015_01_28-AM-00_13_05
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