Nuprl Lemma : State-loc-comb-classrel-mem
∀[Info,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E.
∀[v:B]. (v ∈ Prior(State-loc-comb(init;f;X))?init(e) ⇐⇒ v ∈ Memory-loc-class(f;init;X)(e))
Proof
Definitions occuring in Statement :
State-loc-comb: State-loc-comb(init;f;X),
Memory-loc-class: Memory-loc-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-loc-comb_wf,
Memory-loc-class_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
Id_wf,
bag_wf,
Memory-classrel-loc,
primed-class-opt-classrel,
sq_stable__classrel,
Memory-class_wf,
es-loc_wf,
State-loc-comb-classrel-non-loc,
State-comb-classrel-mem,
State-comb_wf,
and_wf,
equal_wf,
squash_wf,
exists_wf,
es-locl_wf,
es-p-local-pred_wf,
all_wf,
not_wf,
bag-member_wf
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} 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-loc-comb(init;f;X))?init(e) \mLeftarrow{}{}\mRightarrow{} v \mmember{} Memory-loc-class(f;init;X)(e))
Date html generated:
2015_07_22-PM-00_23_25
Last ObjectModification:
2015_01_28-AM-10_15_05
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