Nuprl Lemma : simple-loc-comb-2-concat-single-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B,C:Type]. ∀[F:Id ─→ A ─→ B ─→ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
single-valued-classrel(es;F@Loc o (Loc,X, Y);C)
supposing (∀i:Id. ∀a:A. ∀b:B. (#(F i a b) ≤ 1)) ∧ single-valued-classrel(es;X;A) ∧ single-valued-classrel(es;Y;B)
Proof
Definitions occuring in Statement :
concat-lifting-loc-2: f@Loc,
simple-loc-comb-2: F o (Loc,X, Y),
single-valued-classrel: single-valued-classrel(es;X;T),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
simple-loc-comb-2-concat-classrel,
es-loc_wf,
decidable__le,
bag-size_wf,
event-ordering+_subtype,
nat_wf,
equal-wf-T-base,
false_wf,
not-le-2,
decidable__equal_int,
not-equal-2,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
zero-add,
add_functionality_wrt_le,
add-associates,
le-add-cancel2,
add-swap,
or_wf,
le_wf,
bag-size-zero,
bag-member-empty-iff,
bag-member_wf,
classrel_wf,
bag-size-one,
bag-only_wf2,
single-valued-bag-if-le1,
decidable__lt,
le_antisymmetry_iff,
add-zero,
le-add-cancel,
bag-member-single,
single-bag_wf,
simple-loc-comb-2_wf,
concat-lifting-loc-2_wf,
es-E_wf,
all_wf,
Id_wf,
eclass_wf,
event-ordering+_wf,
bag_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)].
single-valued-classrel(es;F@Loc o (Loc,X, Y);C)
supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. (\#(F i a b) \mleq{} 1))
\mwedge{} single-valued-classrel(es;X;A)
\mwedge{} single-valued-classrel(es;Y;B)
Date html generated:
2015_07_22-PM-00_15_53
Last ObjectModification:
2015_01_28-AM-10_45_40
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