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)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
all: ∀x:A. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
class-opt-class: X?Y,
or: P ∨ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
bfalse: ff,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
sq_stable: SqStable(P),
bool: 𝔹,
unit: Unit,
it: ⋅,
false: False
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:
2016_05_17-AM-09_16_09
Last ObjectModification:
2016_01_17-PM-11_14_21
Theory : classrel!lemmas
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