Nuprl Lemma : iseg-local-property
∀[Info:Type]
∀L1,L2:(Id × Info) List.
(L1 ≤ L2
⇒ (∀[P:Id ⟶ Info List+ ⟶ ℙ]
∀e:E. (es-local-property(i,L.P[i;L];global-eo(L1);e) ⇐⇒ es-local-property(i,L.P[i;L];global-eo(L2);e))))
Proof
Definitions occuring in Statement :
global-eo: global-eo(L),
es-local-property: es-local-property(i,L.P[i; L];es;e),
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],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: 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,
subtype_rel: A ⊆r B,
prop: ℙ,
uimplies: b supposing a,
top: Top,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
true: True,
es-embedding: (f embeds eo1 into eo2)
Latex:
\mforall{}[Info:Type]
\mforall{}L1,L2:(Id \mtimes{} Info) List.
(L1 \mleq{} L2
{}\mRightarrow{} (\mforall{}[P:Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]
\mforall{}e:E
(es-local-property(i,L.P[i;L];global-eo(L1);e)
\mLeftarrow{}{}\mRightarrow{} es-local-property(i,L.P[i;L];global-eo(L2);e))))
Date html generated:
2016_05_17-AM-08_33_55
Last ObjectModification:
2016_01_17-PM-02_28_03
Theory : event-ordering
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