Nuprl Lemma : State-classrel
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀[v:B]. (v ∈ State-class(init;f;X)(e) ⇐⇒ iterated_classrel(es;B;A;f;init;X;e;v))
Proof
Definitions occuring in Statement :
State-class: State-class(init;f;X),
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-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
bag-null_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
bag_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bag-null,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
classrel_wf,
exists_wf,
Memory-class_wf,
bag-member_wf,
bag-member-empty-iff,
bag-member-lifting-2,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
all_wf,
sq_stable__classrel,
State-class_wf,
equal_wf,
bool_cases_sqequal,
assert-bnot,
empty-bag-iff-no-member
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E.
\mforall{}[v:B]. (v \mmember{} State-class(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} iterated\_classrel(es;B;A;f;init;X;e;v))
Date html generated:
2015_07_22-PM-00_20_19
Last ObjectModification:
2015_01_28-AM-10_14_00
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