Nuprl Lemma : rec-combined-loc-class-opt-1-single-val0
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[F:Id ─→ A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(B)]. ∀[e:E]. ∀[v1,v2:B].
(v1 = v2 ∈ B) supposing
(v1 ∈ lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
v2 ∈ lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Proof
Definitions occuring in Statement :
lifting-loc-2: lifting-loc-2(f),
rec-combined-loc-class-opt-1: F|Loc, X, Prior(self)?init|,
single-valued-classrel: single-valued-classrel(es;X;T),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
classrel_wf,
rec-combined-loc-class-opt-1_wf,
lifting-loc-2_wf,
single-valued-classrel_wf,
single-valued-bag_wf,
es-loc_wf,
nat_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
es-causl_wf,
rec-combined-loc-class-opt-1-classrel,
simple-loc-comb-2-classrel,
primed-class-opt_wf,
primed-class-opt-classrel,
es-locl-trichotomy,
equal_wf,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
event-ordering+_subtype,
es-E_wf,
Id_wf,
bag_wf,
eclass_wf,
event-ordering+_wf,
and_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[F:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}[e:E]. \mforall{}[v1,v2:B].
(v1 = v2) supposing
(v1 \mmember{} lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
v2 \mmember{} lifting-loc-2(F)|Loc, X, Prior(self)?init|(e) and
single-valued-classrel(es;X;A) and
single-valued-bag(init loc(e);B))
Date html generated:
2015_07_22-PM-00_16_52
Last ObjectModification:
2015_01_28-AM-10_44_52
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