Nuprl Lemma : simple-comb1-concat-classrel
∀[Info,B,C:Type]. ∀[f:B ─→ bag(C)]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ λa.concat-lifting1(f;a)|X|(e);↓∃b:B. (b ∈ X(e) ∧ v ↓∈ f b))
Proof
Definitions occuring in Statement :
simple-comb1: λx.F[x]|X|,
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,
concat-lifting1: concat-lifting1(f;bag),
bag-member: x ↓∈ bs,
bag: bag(T)
Lemmas :
int_seg_wf,
bag_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,
bag-member_wf,
concat-lifting1_wf,
false_wf,
lelt_wf,
squash_wf,
exists_wf,
all_wf,
bag-member-union,
bag-combine_wf,
single-bag_wf,
bag-member-combine,
bag-member-single,
subtype_rel-equal,
select-cons-hd,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
zero-add,
add_functionality_wrt_le,
add-associates,
le-add-cancel2,
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
and_wf,
equal_wf,
classrel_wf,
simple-comb_wf,
le_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
es-interface-subtype_rel2
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[f:B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} \mlambda{}a.concat-lifting1(f;a)|X|(e);\mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} v \mdownarrow{}\mmember{} f b))
Date html generated:
2015_07_22-PM-00_10_06
Last ObjectModification:
2015_01_28-AM-11_42_37
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