Nuprl Lemma : iterated-classrel-invariant
∀[Info,A,S:Type]. ∀[init:Id ─→ bag(S)]. ∀[f:A ─→ S ─→ S]. ∀[X:EClass(A)]. ∀[P:S ─→ ℙ].
∀es:EO+(Info). ∀e:E. ∀v:S.
((∀s:S. (s ↓∈ init loc(e) ⇒ P[s]))
⇒ (∀a:A. ∀e':E. ∀s:S.
(e' ≤loc e ⇒ a ∈ X(e') ⇒ prior-iterated-classrel(es;A;S;s;X;f;init;e') ⇒ P[s] ⇒ P[f a s]))
⇒ iterated-classrel(es;S;A;f;init;X;e;v)
⇒ P[v])
Proof
Definitions occuring in Statement :
prior-iterated-classrel: prior-iterated-classrel(es;A;S;s;X;f;init;e),
iterated-classrel: iterated-classrel(es;S;A;f;init;X;e;v),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
es-causl-swellfnd,
less_than_transitivity1,
less_than_irreflexivity,
int_seg_wf,
decidable__equal_int,
subtype_rel-int_seg,
false_wf,
le_weakening,
subtract_wf,
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,
eqff_to_assert,
assert_of_bnot,
iterated-classrel_wf,
all_wf,
es-le_wf,
classrel_wf,
prior-iterated-classrel_wf,
bag-member_wf,
es-loc_wf,
equal_wf,
int_seg_subtype-nat,
decidable__lt,
not-equal-2,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
add-swap,
add-commutes,
add-associates,
add_functionality_wrt_le,
zero-add,
le-add-cancel-alt,
less-iff-le,
le-add-cancel,
set_wf,
less_than_wf,
primrec-wf2,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
es-le-self,
not_wf,
assert_wf,
es-pred_wf,
iff_weakening_equal,
sq_stable__bag-member,
and_wf,
member_wf,
es-pred-locl,
es-causl_weakening,
es-locl_transitivity1,
es-le_weakening,
es-loc-pred
\mforall{}[Info,A,S:Type]. \mforall{}[init:Id {}\mrightarrow{} bag(S)]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. \mforall{}[X:EClass(A)]. \mforall{}[P:S {}\mrightarrow{} \mBbbP{}].
\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:S.
((\mforall{}s:S. (s \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. \mforall{}s:S.
(e' \mleq{}loc e
{}\mRightarrow{} a \mmember{} X(e')
{}\mRightarrow{} prior-iterated-classrel(es;A;S;s;X;f;init;e')
{}\mRightarrow{} P[s]
{}\mRightarrow{} P[f a s]))
{}\mRightarrow{} iterated-classrel(es;S;A;f;init;X;e;v)
{}\mRightarrow{} P[v])
Date html generated:
2015_07_17-PM-00_27_51
Last ObjectModification:
2015_02_04-PM-05_33_04
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