Nuprl Lemma : iterated-classrel-single-val
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v1,v2:S].
(v1 = v2 ∈ S) supposing
(iterated-classrel(es;S;A;f;init;X;e;v2) and
iterated-classrel(es;S;A;f;init;X;e;v1) and
single-valued-bag(init loc(e);S) and
single-valued-classrel(es;X;A))
Proof
Definitions occuring in Statement :
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
single-valued-classrel: single-valued-classrel(es;X;T),
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,
iterated-classrel_wf,
single-valued-bag_wf,
es-loc_wf,
single-valued-classrel_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,
es-first_wf2,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
and_wf,
equal_wf,
eqff_to_assert,
assert_of_bnot,
es-pred_wf,
es-pred-locl,
es-causl_weakening,
squash_wf,
true_wf,
bag_wf,
es-pred-loc-base,
iff_weakening_equal,
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,
eclass_wf,
Id_wf
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v1,v2:S].
(v1 = v2) supposing
(iterated-classrel(es;S;A;f;init;X;e;v2) and
iterated-classrel(es;S;A;f;init;X;e;v1) and
single-valued-bag(init loc(e);S) and
single-valued-classrel(es;X;A))
Date html generated:
2015_07_17-PM-00_26_30
Last ObjectModification:
2015_02_04-PM-05_35_10
Home
Index