Nuprl Lemma : concat-lifting-loc-member
∀[B:Type]. ∀[n:ℕ]. ∀[A:ℕn ─→ Type]. ∀[bags:k:ℕn ─→ bag(A k)]. ∀[f:Id ─→ funtype(n;A;bag(B))]. ∀[b:B]. ∀[l:Id].
(b ↓∈ concat-lifting-loc(n;bags;l;f)
⇐⇒ ↓∃lst:k:ℕn ─→ (A k). ((∀[k:ℕn]. lst k ↓∈ bags k) ∧ b ↓∈ uncurry-rev(n;f l) lst))
Proof
Definitions occuring in Statement :
concat-lifting-loc: concat-lifting-loc(n;bags;loc;f),
Id: Id,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[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,
uncurry-rev: uncurry-rev(n;f),
bag-member: x ↓∈ bs,
bag: bag(T),
funtype: funtype(n;A;T)
Lemmas :
concat-lifting-member,
bag-member_wf,
concat-lifting-loc_wf,
squash_wf,
exists_wf,
int_seg_wf,
uall_wf,
uncurry-rev_wf,
bag_wf,
Id_wf,
funtype_wf,
nat_wf
Latex:
\mforall{}[B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[bags:k:\mBbbN{}n {}\mrightarrow{} bag(A k)]. \mforall{}[f:Id {}\mrightarrow{} funtype(n;A;bag(B))].
\mforall{}[b:B]. \mforall{}[l:Id].
(b \mdownarrow{}\mmember{} concat-lifting-loc(n;bags;l;f)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}lst:k:\mBbbN{}n {}\mrightarrow{} (A k). ((\mforall{}[k:\mBbbN{}n]. lst k \mdownarrow{}\mmember{} bags k) \mwedge{} b \mdownarrow{}\mmember{} uncurry-rev(n;f l) lst))
Date html generated:
2015_07_22-PM-00_08_02
Last ObjectModification:
2015_01_28-AM-11_42_02
Home
Index