Nuprl Lemma : rec-class-unique
∀[Info,T:Type]. ∀[G:es:EO+(Info) ⟶ E ⟶ bag(T)]. ∀[F:es:EO+(Info) ⟶ e':E ⟶ T ⟶ {e:E| (e' <loc e)} ⟶ bag(T)].
∀[X:EClass(T)].
X = RecClass(first e G[es;e]or next e after e' with value v F[es;e';v;e]) ∈ EClass(T)
supposing ∀es:EO+(Info). ∀e:E.
((X es e) = if e ∈b prior(X) then let e' = prior(X)(e) in F[es;e';X(e');e] else G[es;e] fi ∈ bag(T))
Proof
Definitions occuring in Statement :
es-rec-class: es-rec-class,
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
ifthenelse: if b then t else f fi ,
let: let,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_apply: x[s],
so_apply: x[s1;s2;s3;s4],
let: let,
strongwellfounded: SWellFounded(R[x; y]),
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
less_than: a < b,
squash: ↓T,
es-rec-class: es-rec-class,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
in-eclass: e ∈b X,
true: True,
es-E-interface: E(X),
es-locl: (e <loc e'),
eclass-val: X(e),
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}[Info,T:Type]. \mforall{}[G:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} bag(T)]. \mforall{}[F:es:EO+(Info)
{}\mrightarrow{} e':E
{}\mrightarrow{} T
{}\mrightarrow{} \{e:E| (e' <loc e)\}
{}\mrightarrow{} bag(T)]. \mforall{}[X:EClass(T)].
X = RecClass(first e G[es;e]or next e after e' with value v F[es;e';v;e])
supposing \mforall{}es:EO+(Info). \mforall{}e:E.
((X es e)
= if e \mmember{}\msubb{} prior(X) then let e' = prior(X)(e) in F[es;e';X(e');e] else G[es;e] fi )
Date html generated:
2016_05_17-AM-06_35_41
Last ObjectModification:
2016_01_17-PM-06_42_43
Theory : event-ordering
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