Nuprl Lemma : es-interface-predecessors-cases
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(e) ~ if e ∈b X then if first(e) then [e] else ≤(X)(pred(e)) @ [e] fi
if first(e) then []
else ≤(X)(pred(e))
fi )
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
append: as @ bs,
cons: [a / b],
nil: [],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-interface-predecessors: ≤(X)(e),
es-le-before: ≤loc(e),
eclass-events: eclass-events(es;X;L),
es-before: before(e),
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
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 ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) \msim{} if e \mmember{}\msubb{} X then if first(e) then [e] else \mleq{}(X)(pred(e)) @ [e] fi
if first(e) then []
else \mleq{}(X)(pred(e))
fi )
Date html generated:
2016_05_16-PM-11_02_17
Last ObjectModification:
2015_12_29-AM-10_41_00
Theory : event-ordering
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