Nuprl Lemma : iseg-local-relation
∀[Info:Type]
∀L1,L2:(Id × Info) List.
(L1 ≤ L2
⇒ (∀[R:Id ─→ Id ─→ Info List+ ─→ Info List+ ─→ ℙ]
∀e1,e2:E.
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L1);e1;e2)
⇐⇒ es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L2);e1;e2))))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2),
es-E: E,
Id: Id,
iseg: l1 ≤ l2,
listp: A List+,
list: T 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,
function: x:A ─→ B[x],
product: x:A × B[x],
universe: Type
Lemmas :
iseg-es-embedding,
embedding-preserves-local-relation,
global-eo_wf,
es-E_wf,
event-ordering+_subtype,
Id_wf,
listp_wf,
iseg_wf,
list_wf,
iseg_length,
global-eo-E-sq,
true_wf,
int_seg_wf,
length_wf,
less_than_transitivity1,
lelt_wf
Latex:
\mforall{}[Info:Type]
\mforall{}L1,L2:(Id \mtimes{} Info) List.
(L1 \mleq{} L2
{}\mRightarrow{} (\mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]
\mforall{}e1,e2:E.
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L1);e1;e2)
\mLeftarrow{}{}\mRightarrow{} es-local-relation(i,j,L1,L2.R[i;j;L1;L2];global-eo(L2);e1;e2))))
Date html generated:
2015_07_21-PM-04_38_41
Last ObjectModification:
2015_01_27-PM-05_03_37
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