Nuprl Lemma : State-comb-classrel2
∀[Info,B,A:Type]. ∀[f:A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)].
∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀[v:B]. (v ∈ State-comb(init;f;X)(e) ⇐⇒ ↓iterated-classrel(es;B;A;f;init;X;e;v))
Proof
Definitions occuring in Statement :
State-comb: State-comb(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,
squash: ↓T,
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
State-classrel2,
State-comb-classrel-class,
classrel_wf,
State-comb_wf,
iff_wf,
State-class_wf,
squash_wf,
iterated-classrel_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
Id_wf,
bag_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{} State-comb(init;f;X)(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}iterated-classrel(es;B;A;f;init;X;e;v))
Date html generated:
2015_07_22-PM-00_21_15
Last ObjectModification:
2015_01_28-AM-10_11_57
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