Nuprl Lemma : class-opt-class-classrel
∀[Info,T:Type]. ∀[X,Y:EClass(T)]. ∀[v:T]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(v ∈ X?Y(e);↓((↑bag-null(X es e)) ∧ v ∈ Y(e)) ∨ ((¬↑bag-null(X es e)) ∧ v ∈ X(e)))
Proof
Definitions occuring in Statement :
class-opt-class: X?Y,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
squash: ↓T,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
universe: Type,
bag-null: bag-null(bs)
Lemmas :
classrel_wf,
class-opt-class_wf,
squash_wf,
or_wf,
assert_wf,
bag-null_wf,
not_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
eclass_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-bag-null,
eqff_to_assert,
iff_transitivity,
bnot_wf,
equal-wf-T-base,
bag_wf,
iff_weakening_uiff,
assert_of_bnot,
sq_stable__classrel,
uiff_transitivity
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X,Y:EClass(T)]. \mforall{}[v:T]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(v \mmember{} X?Y(e);\mdownarrow{}((\muparrow{}bag-null(X es e)) \mwedge{} v \mmember{} Y(e)) \mvee{} ((\mneg{}\muparrow{}bag-null(X es e)) \mwedge{} v \mmember{} X(e)))
Date html generated:
2015_07_22-PM-00_08_19
Last ObjectModification:
2015_01_28-AM-11_41_58
Home
Index