Nuprl Lemma : State-comb-classrel-mem
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
∀[v:B]. (v ∈ Prior(State-comb(init;f;X))?init(e) ⇐⇒ v ∈ Memory-class(f;init;X)(e))
Proof
Definitions occuring in Statement :
State-comb: State-comb(init;f;X),
Memory-class: Memory-class(f;init;X),
primed-class-opt: Prior(X)?b,
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 :
classrel_wf,
primed-class-opt_wf,
State-comb_wf,
Memory-class_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
primed-class-opt-classrel,
sq_stable__classrel,
decidable__assert,
es-first_wf2,
btrue_neq_bfalse,
assert_elim,
es-locl-first,
es-loc_wf,
bag-member_wf,
assert_wf,
iff_weakening_equal,
true_wf,
squash_wf,
iterated_classrel_wf,
es-loc-pred,
es-pred_wf,
es-locl-trichotomy,
Memory-classrel,
State-comb-classrel,
es-causl_irreflexivity,
es-causle_weakening,
es-causl_transitivity2,
es-locl_irreflexivity,
es-le_weakening_eq,
es-locl_transitivity2,
es-causl_weakening,
es-pred-locl,
es-pred_property,
less_than_wf,
nat_wf,
bag-size_wf,
equal_wf,
and_wf,
State-comb-exists,
State-comb-exists-iff,
not_wf,
bag-member-iff-size,
es-pred-loc-base,
all_wf,
es-p-local-pred_wf,
exists_wf,
es-locl_wf
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{} Prior(State-comb(init;f;X))?init(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} Memory-class(f;init;X)(e))
Date html generated:
2015_07_22-PM-00_21_20
Last ObjectModification:
2015_07_16-AM-09_39_20
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