Nuprl Lemma : simple-loc-comb-3-concat-single-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B,C,D:Type]. ∀[F:Id ─→ A ─→ B ─→ C ─→ bag(D)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
∀[Z:EClass(C)].
single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D)
supposing (∀i:Id. ∀a:A. ∀b:B. ∀c:C. (#(F i a b c) ≤ 1))
∧ single-valued-classrel(es;X;A)
∧ single-valued-classrel(es;Y;B)
∧ single-valued-classrel(es;Z;C)
Proof
Definitions occuring in Statement :
concat-lifting-loc-3: concat-lifting-loc-3(f),
simple-loc-comb-3: F|Loc, X, Y, Z|,
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 :
bag-member-union,
classrel_wf,
simple-loc-comb-3_wf,
concat-lifting-loc-3_wf,
es-E_wf,
event-ordering+_subtype,
all_wf,
Id_wf,
le_wf,
bag-size_wf,
nat_wf,
eclass_wf,
event-ordering+_wf,
bag_wf,
bag-combine_wf,
single-bag_wf,
es-loc_wf,
bag-member-combine,
bag-member-single,
decidable__le,
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,
bag-size-zero,
bag-member_wf,
squash_wf,
true_wf,
iff_weakening_equal,
bag-member-empty-iff,
bag-size-one,
bag-only_wf2,
single-valued-bag-if-le1,
decidable__lt,
le_antisymmetry_iff,
le-add-cancel,
add-zero,
and_wf,
equal_wf,
single-valued-bag_wf,
less_than_wf,
single-valued-bag-single
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B,C,D:Type]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C {}\mrightarrow{} bag(D)]. \mforall{}[X:EClass(A)].
\mforall{}[Y:EClass(B)]. \mforall{}[Z:EClass(C)].
single-valued-classrel(es;concat-lifting-loc-3(F)|Loc, X, Y, Z|;D)
supposing (\mforall{}i:Id. \mforall{}a:A. \mforall{}b:B. \mforall{}c:C. (\#(F i a b c) \mleq{} 1))
\mwedge{} single-valued-classrel(es;X;A)
\mwedge{} single-valued-classrel(es;Y;B)
\mwedge{} single-valued-classrel(es;Z;C)
Date html generated:
2015_07_22-PM-00_15_43
Last ObjectModification:
2015_02_04-PM-04_40_14
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