Nuprl Lemma : State-comb-es-sv1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[f:A ─→ B ─→ B]. ∀[X:EClass(A)]. ∀[init:Id ─→ bag(B)].
(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],
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 :
rec-comb-es-sv,
false_wf,
le_wf,
int_seg_wf,
select_wf,
cons_wf,
nil_wf,
sq_stable__le,
length_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
bag-null_wf,
lelt_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert-bag-null,
equal-wf-T-base,
bag_wf,
lifting-2_wf,
decidable__equal_int,
int_subtype_base,
bag-size_wf,
nat_wf,
all_wf,
assert_wf,
bnot_wf,
not_wf,
less_than_wf,
State-comb_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
Id_wf,
es-sv-class_wf,
uiff_transitivity,
eqtt_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
bag-size-zero,
decidable__le,
not-le-2,
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,
empty-bag_wf,
bag-size-one,
bag-combine-single-left,
bag-combine_wf,
single-bag_wf,
bag-only_wf2,
single-valued-bag-if-le1,
decidable__lt,
le_antisymmetry_iff,
le-add-cancel,
le_weakening,
bag_combine_empty_lemma,
bag_size_empty_lemma,
add-zero,
bag_size_single_lemma
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[X:EClass(A)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
(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_11
Last ObjectModification:
2015_01_28-AM-10_14_23
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