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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
pairwise: (∀x,y∈L. P[x; y]),
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
less_than: a < b,
squash: ↓T,
es-interface-disjoint: X ⋂ Y = 0,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
glued: glued(es;B;f;Ia;Ib),
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb,
glues: g glues Ia ──f⟶ Ib
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:
2016_05_17-AM-08_02_47
Last ObjectModification:
2016_01_17-PM-02_47_26
Theory : event-ordering
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