Nuprl Lemma : sv-classrel
∀[Info,A:Type]. ∀[X:EClass(A)].
(Singlevalued(X) ⇒ (∀es:EO+(Info). ∀e:E. ∀v:A. (v ∈ X(e) ⇐⇒ (↑e ∈b X) ∧ (v = X(e) ∈ A))))
Proof
Definitions occuring in Statement :
sv-class: Singlevalued(X),
eclass-val: X(e),
in-eclass: e ∈b X,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
squash: ↓T,
eclass-val: X(e),
in-eclass: e ∈b X,
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
nat: ℕ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
true: True,
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
single-bag: {x},
cons: [a / b],
nil: [],
less_than: a < b,
less_than': less_than'(a;b),
nequal: a ≠ b ∈ T
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)].
(Singlevalued(X) {}\mRightarrow{} (\mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:A. (v \mmember{} X(e) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (v = X(e)))))
Date html generated:
2016_05_16-PM-02_20_47
Last ObjectModification:
2016_01_17-PM-07_39_21
Theory : event-ordering
Home
Index