Nuprl Lemma : eclass3-member
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ C)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E].
  uiff(↑e ∈b eclass3(X;Y);(↑e ∈b X) ∧ (↑e ∈b Y))
Proof
Definitions occuring in Statement : 
eclass3: eclass3(X;Y)
, 
member-eclass: e ∈b X
, 
eclass: EClass(A[eo; e])
, 
event-ordering+: EO+(Info)
, 
es-E: E
, 
assert: ↑b
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
, 
rev_implies: P 
⇐ Q
, 
squash: ↓T
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
rev_uimplies: rev_uimplies(P;Q)
, 
cand: A c∧ B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type].  \mforall{}[X:EClass(B  {}\mrightarrow{}  C)].  \mforall{}[Y:EClass(B)].  \mforall{}[es:EO+(Info)].  \mforall{}[e:E].
    uiff(\muparrow{}e  \mmember{}\msubb{}  eclass3(X;Y);(\muparrow{}e  \mmember{}\msubb{}  X)  \mwedge{}  (\muparrow{}e  \mmember{}\msubb{}  Y))
Date html generated:
2016_05_16-PM-02_13_32
Last ObjectModification:
2016_01_17-PM-07_37_30
Theory : event-ordering
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