Nuprl Lemma : simple-loc-comb-1-concat-single-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[F:Id ⟶ A ⟶ bag(B)]. ∀[X:EClass(A)].
(single-valued-classrel(es;F@(Loc, X);B)) supposing
((∀i:Id. ∀a:A. ∀e:E. (a ∈ X(e) ⇒ single-valued-bag(F i a;B))) and
single-valued-classrel(es;X;A))
Proof
Definitions occuring in Statement :
concat-lifting-loc-1: f@,
simple-loc-comb-1: F(Loc, X),
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,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Definitions unfolded in proof :
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
single-valued-bag: single-valued-bag(b;T),
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)].
(single-valued-classrel(es;F@(Loc, X);B)) supposing
((\mforall{}i:Id. \mforall{}a:A. \mforall{}e:E. (a \mmember{} X(e) {}\mRightarrow{} single-valued-bag(F i a;B))) and
single-valued-classrel(es;X;A))
Date html generated:
2016_05_17-AM-09_29_23
Last ObjectModification:
2015_12_29-PM-04_01_41
Theory : classrel!lemmas
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