Nuprl Lemma : Accum-loc-class-exists
∀[Info,B,A:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[f:Id ─→ A ─→ B ─→ B]. ∀[init:Id ─→ bag(B)]. ∀[X:EClass(A)].
((↓∃x:B. x ↓∈ init loc(e)) ⇒ (↓∃u:A. u ∈ X(e)) ⇒ (↓∃v:B. v ∈ Accum-loc-class(f;init;X)(e)))
Proof
Definitions occuring in Statement :
Accum-loc-class: Accum-loc-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
implies: P ⇒ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
primed-class-opt-exists,
Accum-loc-class_wf,
rec-combined-loc-class-opt-1-classrel,
simple-loc-comb-2-classrel,
primed-class-opt_wf,
rec-combined-loc-class-opt-1_wf,
lifting-loc-2_wf,
classrel_wf,
exists_wf,
squash_wf,
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
eclass_wf,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf
Latex:
\mforall{}[Info,B,A:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[init:Id {}\mrightarrow{} bag(B)].
\mforall{}[X:EClass(A)].
((\mdownarrow{}\mexists{}x:B. x \mdownarrow{}\mmember{} init loc(e)) {}\mRightarrow{} (\mdownarrow{}\mexists{}u:A. u \mmember{} X(e)) {}\mRightarrow{} (\mdownarrow{}\mexists{}v:B. v \mmember{} Accum-loc-class(f;init;X)(e)))
Date html generated:
2015_07_22-PM-00_18_06
Last ObjectModification:
2015_01_28-AM-10_42_55
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