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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