Nuprl Lemma : rec-bind-classrel2
∀[Info,A,B:Type]. ∀[X:A ─→ EClass(B)]. ∀[Y:A ─→ EClass(A)].
∀[es:EO+(Info)]. ∀[e:E]. ∀[a:A]. ∀[v:B].
uiff(v ∈ rec-bind-class(X;Y) a(e);↓v ∈ X a(e)
∨ (∃a':A. (a' ∈ Y a(e) ∧ v ∈ X a'(e)))
∨ (∃e':E. ∃a':A. ((e' <loc e) ∧ a' ∈ Y a(e') ∧ v ∈ rec-bind-class(X;Y) a'(e))))
supposing not-self-starting{i:l}(Info;A;Y)
Proof
Definitions occuring in Statement :
rec-bind-class: rec-bind-class(X;Y),
not-self-starting: not-self-starting{i:l}(Info;A;Y),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
sq_stable__uiff,
classrel_wf,
rec-bind-class_wf,
squash_wf,
or_wf,
exists_wf,
eo-forward_wf,
member-eo-forward-E,
es-le-self,
equal_wf,
Id_wf,
es-loc_wf,
es-locl_wf,
es-le_weakening,
sq_stable__classrel,
sq_stable__squash,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
nat_wf,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__lt,
es-causl_wf,
zero-le-nat,
le_wf,
add-mul-special,
zero-mul,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
not-self-starting_wf,
eclass_wf,
parallel-classrel,
mbind-class_wf,
bind-class-rel,
and_wf,
es-le_wf,
true_wf,
iff_weakening_equal,
eo-forward-le,
eo-forward-E-member,
es-le-loc,
es-causle_antisymmetry,
es-causle_weakening_locl,
equal-eo-forward-E,
sq_stable__sq_or
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:A {}\mrightarrow{} EClass(B)]. \mforall{}[Y:A {}\mrightarrow{} EClass(A)].
\mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[a:A]. \mforall{}[v:B].
uiff(v \mmember{} rec-bind-class(X;Y) a(e);\mdownarrow{}v \mmember{} X a(e)
\mvee{} (\mexists{}a':A. (a' \mmember{} Y a(e) \mwedge{} v \mmember{} X a'(e)))
\mvee{} (\mexists{}e':E
\mexists{}a':A
((e' <loc e)
\mwedge{} a' \mmember{} Y a(e')
\mwedge{} v \mmember{} rec-bind-class(X;Y) a'(e))))
supposing not-self-starting\{i:l\}(Info;A;Y)
Date html generated:
2015_07_22-PM-00_27_06
Last ObjectModification:
2015_02_04-PM-05_13_30
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