Nuprl Lemma : primed-classrel-opt
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[b:Id ⟶ bag(T)]. ∀[es:EO+(Info)]. ∀[v:T]. ∀[e:E].
uiff(v ∈ Prior(X)?b(e);↓∃e'<e.v ∈ X(e') ∧ ∀e''<e.∀w:T. (w ∈ X(e'') ⇒ e'' ≤loc e' )
∨ (v ↓∈ b loc(e) ∧ ∀e'<e.∀w:T. (¬w ∈ X(e'))))
Proof
Definitions occuring in Statement :
primed-class-opt: Prior(X)?b,
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-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
squash: ↓T,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
classrel: v ∈ X(e),
primed-class-opt: Prior(X)?b,
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
or: P ∨ Q,
squash: ↓T,
sq_exists: ∃x:{A| B[x]},
bag-member: x ↓∈ bs,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
existse-before: ∃e<e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
alle-lt: ∀e<e'.P[e],
decidable: Dec(P),
not: ¬A,
es-locl: (e <loc e'),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False,
rev_uimplies: rev_uimplies(P;Q),
guard: {T},
sq_stable: SqStable(P),
es-le: e ≤loc e' ,
bag-size: #(bs),
empty-bag: {},
lt_int: i <z j,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[b:Id {}\mrightarrow{} bag(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[v:T]. \mforall{}[e:E].
uiff(v \mmember{} Prior(X)?b(e);\mdownarrow{}\mexists{}e'<e.v \mmember{} X(e') \mwedge{} \mforall{}e''<e.\mforall{}w:T. (w \mmember{} X(e'') {}\mRightarrow{} e'' \mleq{}loc e' )
\mvee{} (v \mdownarrow{}\mmember{} b loc(e) \mwedge{} \mforall{}e'<e.\mforall{}w:T. (\mneg{}w \mmember{} X(e'))))
Date html generated:
2016_05_17-AM-06_32_00
Last ObjectModification:
2016_01_17-PM-06_39_35
Theory : event-ordering
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