Nuprl Lemma : eclass2-single-val
∀[Info,B,C:Type]. ∀[X:EClass(B ─→ bag(C))]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)].
(single-valued-classrel(es;(X o Y);C)) supposing
(single-valued-classrel(es;X;B ─→ bag(C)) and
single-valued-classrel(es;Y;B) and
(∀b:B. ∀cs:bag(C). ∀es:EO+(Info). ∀e:E. (cs ∈ X(b)(e) ⇒ single-valued-bag(cs;C))))
Proof
Definitions occuring in Statement :
eclass2: (X o Y),
class-ap-val: X(v),
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
eclass2-classrel,
equal_wf,
bag-member_wf,
classrel_wf,
bag_wf,
class-ap-val-classrel,
eclass2_wf,
es-E_wf,
event-ordering+_subtype,
single-valued-classrel_wf,
all_wf,
event-ordering+_cumulative2,
class-ap-val_wf,
single-valued-bag_wf,
eclass_wf,
event-ordering+_wf
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)].
(single-valued-classrel(es;(X o Y);C)) supposing
(single-valued-classrel(es;X;B {}\mrightarrow{} bag(C)) and
single-valued-classrel(es;Y;B) and
(\mforall{}b:B. \mforall{}cs:bag(C). \mforall{}es:EO+(Info). \mforall{}e:E. (cs \mmember{} X(b)(e) {}\mRightarrow{} single-valued-bag(cs;C))))
Date html generated:
2015_07_17-PM-00_37_05
Last ObjectModification:
2015_01_27-PM-11_16_19
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