Nuprl Lemma : interface-predecessors-split
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀e:E(X). ∀A,B:E(X) List.
(∃p:E(X)
(p ≤loc e
∧ (≤(X)(p) = A ∈ (E(X) List))
∧ (filter(λa.p <loc a;≤(X)(e)) = B ∈ (E(X) List))
∧ (p <loc e) supposing ¬↑null(B)
∧ (p = last(A) ∈ E))) supposing
((¬↑null(A)) and
(≤(X)(e) = (A @ B) ∈ (E(X) List)))
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-bless: e <loc e',
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
last: last(L),
null: null(as),
filter: filter(P;l),
append: as @ bs,
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
and: P ∧ Q,
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
or: P ∨ Q,
cand: A c∧ B,
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-causl: (e < e'),
squash: ↓T,
es-E-interface: E(X),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
irrefl: Irrefl(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
trans: Trans(T;x,y.E[x; y]),
rev_implies: P ⇐ Q,
decidable: Dec(P),
uiff: uiff(P;Q),
satisfiable_int_formula: satisfiable_int_formula(fmla),
cons: [a / b],
bfalse: ff,
ge: i ≥ j ,
le: A ≤ B
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}e:E(X). \mforall{}A,B:E(X) List.
(\mexists{}p:E(X)
(p \mleq{}loc e
\mwedge{} (\mleq{}(X)(p) = A)
\mwedge{} (filter(\mlambda{}a.p <loc a;\mleq{}(X)(e)) = B)
\mwedge{} (p <loc e) supposing \mneg{}\muparrow{}null(B)
\mwedge{} (p = last(A)))) supposing
((\mneg{}\muparrow{}null(A)) and
(\mleq{}(X)(e) = (A @ B)))
Date html generated:
2016_05_17-AM-07_04_26
Last ObjectModification:
2016_01_17-PM-06_46_27
Theory : event-ordering
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