Nuprl Lemma : loop-class-state-exists
∀[Info,B:Type]. ∀[X:EClass(B ─→ B)]. ∀[init:Id ─→ bag(B)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(0 < #(init loc(e));↓∃v:B. v ∈ loop-class-state(X;init)(e))
Proof
Definitions occuring in Statement :
loop-class-state: loop-class-state(X;init),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Lemmas :
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
bag-size_wf,
es-loc_wf,
member-less_than,
squash_wf,
exists_wf,
classrel_wf,
loop-class-state_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,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
eclass_wf,
decidable__assert,
es-first_wf2,
member-eclass_wf,
bag-member-iff-size,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
eqff_to_assert,
es-p-local-pred_wf,
es-locl_wf,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
primed-class-opt-classrel,
eqtt_to_assert,
bool_wf,
primed-class-opt_wf,
eclass-cond-classrel,
assert-member-eclass,
assert-bnot,
iff_weakening_equal,
es-loc-pred,
true_wf,
es-causl_weakening,
es-pred-locl,
es-pred_wf,
bag-member_wf,
not_wf,
all_wf,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_transitivity2,
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2,
es-pred_property,
assert_of_bnot,
bool_cases,
atom2_subtype_base
Latex:
\mforall{}[Info,B:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} B)]. \mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(0 < \#(init loc(e));\mdownarrow{}\mexists{}v:B. v \mmember{} loop-class-state(X;init)(e))
Date html generated:
2015_07_21-PM-02_33_00
Last ObjectModification:
2015_07_16-AM-09_42_53
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