Nuprl Lemma : bag-member-sv-list
∀T:Type. ∀L:T List.  ∀x:T. (x ↓∈ L 
⇐⇒ (x ∈ L)) supposing single-valued-list(L;T)
Proof
Definitions occuring in Statement : 
single-valued-list: single-valued-list(L;T)
, 
l_member: (x ∈ l)
, 
list: T List
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
universe: Type
, 
bag-member: x ↓∈ bs
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
single-valued-list: single-valued-list(L;T)
, 
implies: P 
⇒ Q
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
bag-member: x ↓∈ bs
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
rev_implies: P 
⇐ Q
, 
l_member: (x ∈ l)
, 
exists: ∃x:A. B[x]
, 
nat: ℕ
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
cand: A c∧ B
, 
bag: bag(T)
, 
quotient: x,y:A//B[x; y]
, 
guard: {T}
, 
or: P ∨ Q
, 
cons: [a / b]
, 
top: Top
, 
decidable: Dec(P)
, 
uiff: uiff(P;Q)
, 
subtract: n - m
, 
true: True
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
ge: i ≥ j 
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
Latex:
\mforall{}T:Type.  \mforall{}L:T  List.    \mforall{}x:T.  (x  \mdownarrow{}\mmember{}  L  \mLeftarrow{}{}\mRightarrow{}  (x  \mmember{}  L))  supposing  single-valued-list(L;T)
Date html generated:
2016_05_17-AM-11_11_10
Last ObjectModification:
2016_01_18-AM-00_10_06
Theory : process-model
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