Nuprl Lemma : simple-loc-comb1-classrel
∀[Info,B,C:Type]. ∀[f:Id ─→ B ─→ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ simple-loc-comb1(l,a.lifting1-loc(f;l;a);X)(e);↓∃b:B. (b ∈ X(e) ∧ (v = (f loc(e) b) ∈ C)))
Proof
Definitions occuring in Statement :
lifting1-loc: lifting1-loc(f;loc;b),
simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X),
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,
equal: s = t ∈ T
Definitions :
uncurry-rev: uncurry-rev(n;f),
uncurry-gen: uncurry-gen(n),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
bfalse: ff,
btrue: tt
Lemmas :
classrel_wf,
simple-loc-comb1_wf,
lifting1-loc_wf,
bag_wf,
Id_wf,
squash_wf,
exists_wf,
es-loc_wf,
event-ordering+_subtype,
es-E_wf,
event-ordering+_wf,
eclass_wf,
simple-loc-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,
lifting-loc-member-simple,
subtype_rel_dep_function,
funtype_wf,
primrec1_lemma,
subtype_rel_self,
bag-member_wf,
all_wf,
lifting-loc-gen-rev_wf,
uall_wf,
iff_wf,
le-add-cancel2,
add-associates,
add_functionality_wrt_le,
zero-add,
minus-zero,
minus-add,
add-commutes,
condition-implies-le,
less-iff-le,
not-le-2,
decidable__le,
select-cons-hd,
subtype_rel-equal,
es-interface-subtype_rel2,
simple-loc-comb_wf
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} simple-loc-comb1(l,a.lifting1-loc(f;l;a);X)(e);\mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} (v = (f loc(e) b))))
Date html generated:
2015_07_22-PM-00_08_38
Last ObjectModification:
2015_02_02-PM-06_56_39
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