Nuprl Lemma : simple-loc-comb2-concat-classrel
∀[Info,A,B,C:Type]. ∀[f:Id ─→ A ─→ B ─→ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ simple-loc-comb2(l,a,b.concat-lifting2-loc(f;a;b;l);X;Y)(e);↓∃a:A
∃b:B
(a ∈ X(e) ∧ b ∈ Y(e) ∧ v ↓∈ f loc(e) a b))
Proof
Definitions occuring in Statement :
concat-lifting2-loc: concat-lifting2-loc(f;abag;bbag;loc),
simple-loc-comb2: simple-loc-comb2(l,a,b.F[l; a; b];X;Y),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
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,
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
simple-loc-comb-concat-classrel,
false_wf,
le_wf,
select_wf,
cons_wf,
nil_wf,
sq_stable__le,
length_wf,
length_nil,
non_neg_length,
length_wf_nil,
length_cons,
length_wf_nat,
int_seg_wf,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
lelt_wf,
concat-lifting2-loc_wf,
bag_wf,
classrel_wf,
simple-loc-comb2_wf,
Id_wf,
squash_wf,
exists_wf,
bag-member_wf,
es-loc_wf,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
eclass_wf,
all_wf,
bag-member-union,
bag-combine_wf,
single-bag_wf,
bag-member-combine,
bag-member-single,
true_wf,
iff_weakening_equal,
sq_stable__bag-member,
lifting-gen-list-rev_wf,
primrec-unroll,
primrec1_lemma,
simple-loc-comb_wf,
and_wf
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} A {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)].
\mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} simple-loc-comb2(l,a,b.concat-lifting2-loc(f;a;b;l);X;Y)(e);\mdownarrow{}\mexists{}a:A
\mexists{}b:B
(a \mmember{} X(e)
\mwedge{} b \mmember{} Y(e)
\mwedge{} v \mdownarrow{}\mmember{} f loc(e) a b))
Date html generated:
2015_07_22-PM-00_09_44
Last ObjectModification:
2015_02_04-PM-04_42_38
Home
Index