Nuprl Lemma : Q-R-glued-first
∀[Info:Type]
∀es:EO+(Info)
∀[Q,R:E ⟶ E ⟶ ℙ]. ∀[A,B:Type].
∀Ias:EClass(A) List. ∀Ibs:EClass(B) List. ∀f:E(first-class(Ias)) ⟶ B.
((∀i:ℕ||Ias||. Ias[i]:Q →─f⟶ Ibs[i]:R)
⇒ first-class(Ias):Q →─f⟶ first-class(Ibs):R
supposing (∀Ia1,Ia2∈Ias. ∀e,e':E.
((¬(Q e e')) ∧ (¬(Q e' e))) supposing ((↑e' ∈b Ia2) and (↑e ∈b Ia1)))) supposi\000Cng
((||Ias|| = ||Ibs|| ∈ ℤ) and
(∀Ib1,Ib2∈Ibs. Ib1 ⋂ Ib2 = 0) and
(∀Ia1,Ia2∈Ias. Ia1 ⋂ Ia2 = 0))
Proof
Definitions occuring in Statement :
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb,
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-E: E,
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],
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
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],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
top: Top,
prop: ℙ,
implies: P ⇒ Q,
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],
false: False,
not: ¬A,
so_apply: x[s],
pairwise: (∀x,y∈L. P[x; y]),
select: L[n],
nil: [],
it: ⋅,
es-interface-disjoint: X ⋂ Y = 0,
cons: [a / b],
ge: i ≥ j ,
le: A ≤ B,
first-class: first-class(L),
less_than: a < b,
squash: ↓T,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
subtract: n - m,
less_than': less_than'(a;b),
nat_plus: ℕ+,
true: True,
cand: A c∧ B,
rel_equivalent: R1 ⇐⇒ R2,
es-interface-predicate: {I},
rel-restriction: R|P,
rel_or: R1 ∨ R2,
infix_ap: x f y,
es-E-interface: E(X),
rev_implies: P ⇐ Q,
Q-R-glued: Ia:Qa →─f⟶ Ib:Rb
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[Q,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \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||. Ias[i]:Q \mrightarrow{}{}f{}\mrightarrow{} Ibs[i]:R)
{}\mRightarrow{} first-class(Ias):Q \mrightarrow{}{}f{}\mrightarrow{} first-class(Ibs):R
supposing (\mforall{}Ia1,Ia2\mmember{}Ias. \mforall{}e,e':E.
((\mneg{}(Q e e')) \mwedge{} (\mneg{}(Q e' e))) supposing
((\muparrow{}e' \mmember{}\msubb{} Ia2) and
(\muparrow{}e \mmember{}\msubb{} Ia1)))) supposing
((||Ias|| = ||Ibs||) and
(\mforall{}Ib1,Ib2\mmember{}Ibs. Ib1 \mcap{} Ib2 = 0) and
(\mforall{}Ia1,Ia2\mmember{}Ias. Ia1 \mcap{} Ia2 = 0))
Date html generated:
2016_05_17-AM-07_57_26
Last ObjectModification:
2016_01_17-PM-03_08_50
Theory : event-ordering
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