Nuprl Lemma : iseg-interface-predecessors
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E(X). ∀L:E(X) List.
(L ≤ ≤(X)(e)
⇐⇒ (↑null(L)) ∨ ((¬↑null(L)) ∧ (∃p:E(X). (p ≤loc e ∧ (L = ≤(X)(p) ∈ (E(X) List)) ∧ (p = last(L) ∈ E)))))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
iseg: l1 ≤ l2,
last: last(L),
null: null(as),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: 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],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
es-E-interface: E(X),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
false: False,
guard: {T},
cand: A c∧ B,
trans: Trans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
sq_type: SQType(T),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
set-equal: set-equal(T;x;y),
irrefl: Irrefl(T;x,y.E[x; y]),
es-le: e ≤loc e' ,
cons: [a / b],
bfalse: ff
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E(X). \mforall{}L:E(X) List.
(L \mleq{} \mleq{}(X)(e)
\mLeftarrow{}{}\mRightarrow{} (\muparrow{}null(L)) \mvee{} ((\mneg{}\muparrow{}null(L)) \mwedge{} (\mexists{}p:E(X). (p \mleq{}loc e \mwedge{} (L = \mleq{}(X)(p)) \mwedge{} (p = last(L))))))
Date html generated:
2016_05_17-AM-07_04_02
Last ObjectModification:
2015_12_29-AM-00_18_07
Theory : event-ordering
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