Nuprl Lemma : es-interface-predecessors-general-step
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(e)
= (if e ∈b prior(X) then ≤(X)(prior(X)(e)) else [] fi @ if e ∈b X then [e] else [] 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),
es-E: 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,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
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],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-interface-predecessors: ≤(X)(e),
eclass-events: eclass-events(es;X;L),
es-le-before: ≤loc(e),
top: Top,
squash: ↓T,
true: True,
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,
es-before: before(e),
iff: P ⇐⇒ Q,
rev_uimplies: rev_uimplies(P;Q),
rev_implies: P ⇐ Q,
cand: A c∧ B
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) = (if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) else [] fi @ if e \mmember{}\msubb{} X then [e] else [] fi ))
Date html generated:
2016_05_17-AM-06_53_09
Last ObjectModification:
2016_01_17-PM-06_41_00
Theory : event-ordering
Home
Index