Nuprl Lemma : loop-class-state-single-val
∀[Info,B:Type]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(B ─→ B)]. ∀[es:EO+(Info)].
(single-valued-classrel(es;loop-class-state(X;init);B)) supposing
((∀l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B ─→ B))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
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],
all: ∀x:A. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
single-valued-bag: single-valued-bag(b;T),
bag: bag(T)
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
classrel_wf,
loop-class-state_wf,
es-E_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,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
loop-class-state-classrel,
member-eclass_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
es-first_wf2,
es-loc_wf,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
all_wf,
Id_wf,
single-valued-bag_wf,
single-valued-classrel_wf,
event-ordering+_wf,
eclass_wf,
bag_wf,
and_wf,
bag-member_wf
Latex:
\mforall{}[Info,B:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[es:EO+(Info)].
(single-valued-classrel(es;loop-class-state(X;init);B)) supposing
((\mforall{}l:Id. single-valued-bag(init l;B)) and
single-valued-classrel(es;X;B {}\mrightarrow{} B))
Date html generated:
2015_07_21-PM-02_33_42
Last ObjectModification:
2015_01_27-PM-09_48_44
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