Nuprl Lemma : loc-on-path-decomp
∀[Info:Type]
∀es:EO+(Info). ∀Sys:EClass(Top). ∀L:E(Sys) List. ∀j:Id.
(loc-on-path(es;j;L)
⇒ (∃u:E(Sys)
∃A,B:E(Sys) List. ((loc(u) = j ∈ Id) ∧ (L = (A @ [u / B]) ∈ (E(Sys) List)) ∧ (¬loc-on-path(es;j;A)))))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
loc-on-path: loc-on-path(es;i;L),
es-loc: loc(e),
Id: Id,
append: as @ bs,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
es-E-interface: E(X),
and: P ∧ Q,
top: Top,
so_apply: x[s],
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
false: False,
decidable: Dec(P),
or: P ∨ Q,
cand: A c∧ B,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
not: ¬A,
squash: ↓T,
true: True
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}Sys:EClass(Top). \mforall{}L:E(Sys) List. \mforall{}j:Id.
(loc-on-path(es;j;L)
{}\mRightarrow{} (\mexists{}u:E(Sys). \mexists{}A,B:E(Sys) List. ((loc(u) = j) \mwedge{} (L = (A @ [u / B])) \mwedge{} (\mneg{}loc-on-path(es;j;A)))))
Date html generated:
2016_05_16-PM-10_20_15
Last ObjectModification:
2016_01_17-PM-07_29_42
Theory : event-ordering
Home
Index