Nuprl Lemma : simple-comb2-classrel
∀[Info,A,B,C:Type]. ∀[f:A ─→ B ─→ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ λa,b.lifting2(f;a;b)|X;Y|(e);↓∃a:A. ∃b:B. ((a ∈ X(e) ∧ b ∈ Y(e)) ∧ (v = (f a b) ∈ C)))
Proof
Definitions occuring in Statement :
simple-comb2: λx,y.F[x; y]|X;Y|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
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,
lifting2: lifting2(f;abag;bbag)
Lemmas :
simple-comb-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,
lifting2_wf,
bag_wf,
classrel_wf,
simple-comb2_wf,
squash_wf,
exists_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
all_wf,
bag-member_wf,
bag-member-single,
single-bag_wf,
bag-combine_wf,
bag-member-combine,
simple-comb_wf,
less-iff-le,
add-swap,
le-add-cancel2,
add-associates,
minus-zero,
minus-add,
add-commutes,
condition-implies-le,
le-add-cancel,
add-zero,
zero-add,
add_functionality_wrt_le,
not-equal-2,
and_wf,
es-interface-subtype_rel2,
equal_wf
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:C].
uiff(v \mmember{} \mlambda{}a,b.lifting2(f;a;b)|X;Y|(e);\mdownarrow{}\mexists{}a:A. \mexists{}b:B. ((a \mmember{} X(e) \mwedge{} b \mmember{} Y(e)) \mwedge{} (v = (f a b))))
Date html generated:
2015_07_22-PM-00_10_48
Last ObjectModification:
2015_01_30-AM-01_48_48
Home
Index