Nuprl Lemma : glued-first
∀[Info:Type]
∀es:EO+(Info)
∀[A,B:Type].
∀Ias:EClass(A) List. ∀Ibs:EClass(B) List. ∀f:E(first-class(Ias)) ─→ B.
((∀i:ℕ||Ias||. glued(es;B;f;Ias[i];Ibs[i]))
⇒ glued(es;B;f;first-class(Ias);first-class(Ibs))) supposing
((||Ias|| = ||Ibs|| ∈ ℤ) and
(∀Ib1,Ib2∈Ibs. Ib1 ∩ Ib2 = 0) and
(∀Ia1,Ia2∈Ias. ∀es:EO+(Info). ∀e,e':E. (¬(loc(e) = loc(e') ∈ Id)) supposing ((↑e' ∈b Ia2) and (↑e ∈b Ia1)))\000C)
Proof
Definitions occuring in Statement :
glued: glued(es;B;f;Ia;Ib)
,
es-interface-disjoint: X ∩ Y = 0
,
es-E-interface: E(X)
,
first-class: first-class(L)
,
in-eclass: e ∈b X
,
eclass: EClass(A[eo; e])
,
event-ordering+: EO+(Info)
,
es-loc: loc(e)
,
es-E: E
,
Id: Id
,
pairwise: (∀x,y∈L. P[x; y])
,
select: L[n]
,
length: ||as||
,
list: T List
,
int_seg: {i..j-}
,
assert: ↑b
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
all: ∀x:A. B[x]
,
not: ¬A
,
implies: P
⇒ Q
,
function: x:A ─→ B[x]
,
natural_number: $n
,
int: ℤ
,
universe: Type
,
equal: s = t ∈ T
Lemmas :
glued-Q-R-glued,
first-class_wf,
assert_wf,
in-eclass_wf,
select_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
sq_stable__le,
less_than_transitivity2,
length_wf,
event-ordering+_wf,
le_weakening2,
es-interface-subtype_rel2,
top_wf,
int_seg_wf,
es-loc_wf,
es-le-loc,
es-le_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type].
\mforall{}Ias:EClass(A) List. \mforall{}Ibs:EClass(B) List. \mforall{}f:E(first-class(Ias)) {}\mrightarrow{} B.
((\mforall{}i:\mBbbN{}||Ias||. glued(es;B;f;Ias[i];Ibs[i]))
{}\mRightarrow{} glued(es;B;f;first-class(Ias);first-class(Ibs))) supposing
((||Ias|| = ||Ibs||) and
(\mforall{}Ib1,Ib2\mmember{}Ibs. Ib1 \mcap{} Ib2 = 0) and
(\mforall{}Ia1,Ia2\mmember{}Ias. \mforall{}es:EO+(Info). \mforall{}e,e':E.
(\mneg{}(loc(e) = loc(e'))) supposing ((\muparrow{}e' \mmember{}\msubb{} Ia2) and (\muparrow{}e \mmember{}\msubb{} Ia1))))
Date html generated:
2015_07_21-PM-04_16_12
Last ObjectModification:
2015_01_27-PM-05_23_22
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