Nuprl Lemma : bag-member-lifting-loc-2
∀[C,B,A:Type]. ∀[f:Id ─→ A ─→ B ─→ C]. ∀[as:bag(A)]. ∀[bs:bag(B)]. ∀[i:Id]. ∀[c:C].
uiff(c ↓∈ lifting-loc-2(f) i as bs;↓∃a:A. ∃b:B. (a ↓∈ as ∧ b ↓∈ bs ∧ (c = (f i a b) ∈ C)))
Proof
Definitions occuring in Statement :
lifting-loc-2: lifting-loc-2(f),
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
bag-member_wf,
lifting-loc-2_wf,
squash_wf,
exists_wf,
Id_wf,
bag_wf,
bag-member-combine,
bag-combine_wf,
single-bag_wf,
bag-member-single,
sq_stable__bag-member
Latex:
\mforall{}[C,B,A:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[as:bag(A)]. \mforall{}[bs:bag(B)]. \mforall{}[i:Id]. \mforall{}[c:C].
uiff(c \mdownarrow{}\mmember{} lifting-loc-2(f) i as bs;\mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mdownarrow{}\mmember{} as \mwedge{} b \mdownarrow{}\mmember{} bs \mwedge{} (c = (f i a b))))
Date html generated:
2015_07_22-PM-00_07_53
Last ObjectModification:
2015_01_28-AM-11_42_26
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