Nuprl Lemma : three-intersection-two-intersection
∀A:Id List. ∀W:{a:Id| (a ∈ A)}  List List.  (three-intersection(A;W) 
⇒ two-intersection(A;W))
Proof
Definitions occuring in Statement : 
three-intersection: three-intersection(A;W)
, 
two-intersection: two-intersection(A;W)
, 
Id: Id
, 
l_member: (x ∈ l)
, 
list: T List
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
set: {x:A| B[x]} 
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
three-intersection: three-intersection(A;W)
, 
two-intersection: two-intersection(A;W)
, 
l_all: (∀x∈L.P[x])
, 
member: t ∈ T
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
prop: ℙ
, 
uall: ∀[x:A]. B[x]
, 
int_seg: {i..j-}
, 
uimplies: b supposing a
, 
guard: {T}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
false: False
, 
not: ¬A
, 
top: Top
, 
less_than: a < b
, 
squash: ↓T
Latex:
\mforall{}A:Id  List.  \mforall{}W:\{a:Id|  (a  \mmember{}  A)\}    List  List.    (three-intersection(A;W)  {}\mRightarrow{}  two-intersection(A;W))
Date html generated:
2016_05_16-PM-00_01_17
Last ObjectModification:
2016_01_17-PM-03_52_11
Theory : event-ordering
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