Nuprl Lemma : classfun-res-parallel-class-left
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(A)]. ∀[e:E].
(X || Y@e ~ X@e) supposing (disjoint-classrel(es;A;X;A;Y) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
parallel-class: X || Y,
classfun-res: X@e,
disjoint-classrel: disjoint-classrel(es;A;X;B;Y),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
assert-member-eclass,
empty-bag-iff-no-member,
equal-empty-bag,
bag-append-empty,
bag-subtype-list,
disjoint-classrel_wf,
assert_wf,
member-eclass_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(A)]. \mforall{}[e:E].
(X || Y@e \msim{} X@e) supposing (disjoint-classrel(es;A;X;A;Y) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2015_07_23-AM-11_29_01
Last ObjectModification:
2015_01_28-PM-11_12_55
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