Nuprl Lemma : State-comb-es-sv
∀[Info,A:Type]. ∀[es:EO+(Info)]. ∀[f:Top]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(Top)].
(es-sv-class(es;State-comb(init;f;X))) supposing ((∀l:Id. (#(init l) ≤ 1)) and es-sv-class(es;X))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
less_than_wf,
bag-size_wf,
top_wf,
State-comb_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
nat_wf,
all_wf,
Id_wf,
le_wf,
es-sv-class_wf,
bag_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
int_seg_wf,
int_seg_subtype-nat,
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__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
bag-null_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
uiff_transitivity,
eqtt_to_assert,
assert-bag-null,
iff_transitivity,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
primed-class-opt-es-sv0,
es-locl_wf,
es-loc_wf,
bag-size-zero,
minus-zero,
le-add-cancel2,
empty-bag_wf,
bag-size-one,
bag-combine-single-left,
bag-combine_wf,
primed-class-opt_wf,
single-bag_wf,
bag-only_wf2,
single-valued-bag-if-le1,
le_antisymmetry_iff,
bag-combine-single-right-as-map,
bag-size-map
Latex:
\mforall{}[Info,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:Top]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(Top)].
(es-sv-class(es;State-comb(init;f;X))) supposing ((\mforall{}l:Id. (\#(init l) \mleq{} 1)) and es-sv-class(es;X))
Date html generated:
2015_07_22-PM-00_22_18
Last ObjectModification:
2015_01_28-AM-10_13_07
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