Nuprl Lemma : es-rec-class_wf
∀[Info,T:Type]. ∀[G:es:EO+(Info) ⟶ E ⟶ bag(T)]. ∀[F:es:EO+(Info) ⟶ e':E ⟶ T ⟶ {e:E| (e' <loc e)} ⟶ bag(T)].
(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]) ∈ EClass(T))
Proof
Definitions occuring in Statement :
es-rec-class: es-rec-class,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2;s3;s4],
so_apply: x[s1;s2],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
eclass: EClass(A[eo; e]),
top: Top,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-rec-class: es-rec-class,
eclass-val: X(e),
es-prior-interface: prior(X),
in-eclass: e ∈b X,
local-pred-class: local-pred-class(P),
let: let,
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
so_apply: x[s1;s2],
so_apply: x[s1;s2;s3;s4],
sq_exists: ∃x:{A| B[x]},
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
cand: A c∧ B
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)].
(RecClass(first e
G[es;e]
or next e after e' with value v
F[es;e';v;e]) \mmember{} EClass(T))
Date html generated:
2016_05_17-AM-06_29_17
Last ObjectModification:
2016_01_17-PM-06_43_53
Theory : event-ordering
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