Nuprl Lemma : simple-loc-comb-classrel
∀[Info,B:Type]. ∀[n:ℕ]. ∀[A:ℕn ─→ Type]. ∀[Xs:k:ℕn ─→ EClass(A k)]. ∀[f:Id ─→ (k:ℕn ─→ (A k)) ─→ B]. ∀[F:Id
─→ (k:ℕn
─→ bag(A k))
─→ bag(B)].
∀[es:EO+(Info)]. ∀[e:E]. ∀[v:B].
uiff(v ∈ F|Loc; Xs|(e);↓∃vs:k:ℕn ─→ (A k). ((∀k:ℕn. vs[k] ∈ Xs[k](e)) ∧ (v = (f loc(e) vs) ∈ B)))
supposing ∀x:Id. ∀v:B. ∀bs:k:ℕn ─→ bag(A k).
(v ↓∈ F x bs ⇐⇒ ↓∃vs:k:ℕn ─→ (A k). ((∀k:ℕn. vs k ↓∈ bs k) ∧ (v = (f x vs) ∈ B)))
Proof
Definitions occuring in Statement :
simple-loc-comb: F|Loc; Xs|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
int_seg: {i..j-},
nat: ℕ,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
classrel_wf,
simple-loc-comb_wf,
squash_wf,
exists_wf,
int_seg_wf,
all_wf,
es-loc_wf,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
Id_wf,
bag_wf,
iff_wf,
bag-member_wf,
eclass_wf,
nat_wf
\mforall{}[Info,B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[Xs:k:\mBbbN{}n {}\mrightarrow{} EClass(A k)]. \mforall{}[f:Id {}\mrightarrow{} (k:\mBbbN{}n {}\mrightarrow{} (A k)) {}\mrightarrow{} B].
\mforall{}[F:Id {}\mrightarrow{} (k:\mBbbN{}n {}\mrightarrow{} bag(A k)) {}\mrightarrow{} bag(B)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:B].
uiff(v \mmember{} F|Loc; Xs|(e);\mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. vs[k] \mmember{} Xs[k](e)) \mwedge{} (v = (f loc(e) vs))))
supposing \mforall{}x:Id. \mforall{}v:B. \mforall{}bs:k:\mBbbN{}n {}\mrightarrow{} bag(A k).
(v \mdownarrow{}\mmember{} F x bs \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}vs:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}k:\mBbbN{}n. vs k \mdownarrow{}\mmember{} bs k) \mwedge{} (v = (f x vs))))
Date html generated:
2015_07_17-PM-00_46_47
Last ObjectModification:
2015_01_27-PM-11_07_01
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