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
Lemmas :
list_induction,
eclass_wf,
all_wf,
list_wf,
es-E_wf,
event-ordering+_subtype,
es-E-interface_wf,
first-class_wf,
top_wf,
subtype_rel_list,
es-interface-subtype_rel2,
isect_wf,
pairwise_wf,
es-interface-disjoint_wf,
length_wf,
int_seg_wf,
Q-R-glued_wf,
select_wf,
sq_stable__le,
less_than_transitivity1,
le_weakening,
subtype_rel_dep_function,
es-E-interface-first-class,
assert_wf,
in-eclass_wf,
not_wf,
event-ordering+_wf,
length_of_nil_lemma,
stuck-spread,
base_wf,
list-cases,
less_than_irreflexivity,
equal-wf-base,
product_subtype_list,
length_of_cons_lemma,
cons_wf,
length_cons,
non_neg_length,
length_wf_nat,
equal-wf-base-T,
nil_wf,
Q-R-glued-empty,
reduce_nil_lemma,
equal_wf,
le_weakening2,
less_than_transitivity2,
reduce_cons_lemma,
es-E-interface-conditional-subtype2,
cond-class_wf,
pairwise-cons,
lelt_wf,
select_cons_tl_sq,
Q-R-glued-conditional,
subtype_rel_self,
l_all_iff,
l_member_wf,
l_exists_iff,
is-first-class,
or_wf,
es-interface-conditional-domain-iff,
decidable__assert,
Q-R-glues_functionality,
Q-R-glues_wf,
es-interface-predicate_wf,
rel-restriction_wf,
rel_or_wf
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:
2015_07_21-PM-04_13_22
Last ObjectModification:
2015_02_02-PM-06_44_51
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