Nuprl Lemma : class-pred-cases
∀[Info,T:Type].
∀X:EClass(T). ∀es:EO+(Info). ∀e:E.
(∃e'<e.((↓∃v:T. v ∈ X(e')) ∧ ∀e''<e.(↓∃v:T. v ∈ X(e'')) ⇒ e'' ≤loc e' )
∧ (class-pred(X;es;e) = (inl e') ∈ (E + Top))
∨ (∀e'<e.∀v:T. (¬v ∈ X(e')) ∧ (class-pred(X;es;e) = (inr ⋅ ) ∈ (E + Top))))
Proof
Definitions occuring in Statement :
class-pred: class-pred(X;es;e),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
alle-lt: ∀e<e'.P[e],
existse-before: ∃e<e'.P[e],
es-le: e ≤loc e' ,
es-E: E,
it: ⋅,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
inr: inr x ,
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
class-pred: class-pred(X;es;e),
eclass: EClass(A[eo; e]),
or: P ∨ Q,
sq_exists: ∃x:{A| B[x]},
guard: {T},
cand: A c∧ B,
top: Top,
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
existse-before: ∃e<e'.P[e],
sq_stable: SqStable(P),
classrel: v ∈ X(e),
alle-lt: ∀e<e'.P[e],
decidable: Dec(P),
false: False,
not: ¬A,
es-locl: (e <loc e'),
rev_uimplies: rev_uimplies(P;Q),
bag-member: x ↓∈ bs
Latex:
\mforall{}[Info,T:Type].
\mforall{}X:EClass(T). \mforall{}es:EO+(Info). \mforall{}e:E.
(\mexists{}e'<e.((\mdownarrow{}\mexists{}v:T. v \mmember{} X(e')) \mwedge{} \mforall{}e''<e.(\mdownarrow{}\mexists{}v:T. v \mmember{} X(e'')) {}\mRightarrow{} e'' \mleq{}loc e' )
\mwedge{} (class-pred(X;es;e) = (inl e'))
\mvee{} (\mforall{}e'<e.\mforall{}v:T. (\mneg{}v \mmember{} X(e')) \mwedge{} (class-pred(X;es;e) = (inr \mcdot{} ))))
Date html generated:
2016_05_16-PM-11_19_27
Last ObjectModification:
2016_01_17-PM-07_25_49
Theory : event-ordering
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