Nuprl Lemma : es-interface-predecessors-step
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E(X)].
(≤(X)(e) = if e ∈b prior(X) then ≤(X)(prior(X)(e)) @ [e] else [e] fi ∈ ({a:E(X)| loc(a) = loc(e) ∈ Id} List))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
es-E-interface: E(X),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
iff: P ⇐⇒ Q,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)].
(\mleq{}(X)(e) = if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) @ [e] else [e] fi )
Date html generated:
2016_05_17-AM-06_53_57
Last ObjectModification:
2015_12_29-AM-00_18_23
Theory : event-ordering
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