Nuprl Lemma : rec-class-val
∀[Info,T:Type]. ∀[G:es:EO+(Info) ⟶ E ⟶ bag(T)]. ∀[F:es:EO+(Info) ⟶ e':E ⟶ T ⟶ {e:E| (e' <loc e)} ⟶ bag(T)].
∀[es:EO+(Info)]. ∀[e:E].
RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e)
= if e ∈b prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
only(F[es;e';RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e');e])
else only(G[es;e])
fi
∈ T
supposing ↑e ∈b RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
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,
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
assert: ↑b,
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],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
es-rec-class: es-rec-class,
eclass-val: X(e),
let: let,
in-eclass: e ∈b X,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
prop: ℙ,
implies: P ⇒ Q,
uimplies: b supposing a,
guard: {T},
top: Top,
eclass: EClass(A[eo; e]),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
squash: ↓T,
true: True,
rev_uimplies: rev_uimplies(P;Q),
es-locl: (e <loc e'),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
nequal: a ≠ b ∈ T ,
ge: i ≥ j
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{}[es:EO+(Info)]. \mforall{}[e:E].
RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e)
= if e \mmember{}\msubb{} prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))
then let e' = prior(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]))(e) in
only(F[es;e';RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])(e');e])
else only(G[es;e])
fi
supposing \muparrow{}e \mmember{}\msubb{} RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e])
Date html generated:
2016_05_17-AM-06_29_57
Last ObjectModification:
2016_01_17-PM-06_43_32
Theory : event-ordering
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