Nuprl Lemma : eo-forward-no-classrel-in-interval
∀[Info,T:Type]. ∀[X:EClass(T)]. ∀[es:EO+(Info)]. ∀[start:E]. ∀[e1:E]. ∀[e:E].
uiff((no X between e1 and e);(no X between e1 and e)) supposing (loc(e) = loc(e1) ∈ Id) ∧ (loc(e1) = loc(start) ∈ Id)
Proof
Definitions occuring in Statement :
no-classrel-in-interval: (no X between start and e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
no-classrel-in-interval: (no X between start and e),
alle-lt: ∀e<e'.P[e],
not: ¬A,
false: False,
prop: ℙ,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True,
squash: ↓T,
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_apply: x[s]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[X:EClass(T)]. \mforall{}[es:EO+(Info)]. \mforall{}[start:E]. \mforall{}[e1:E]. \mforall{}[e:E].
uiff((no X between e1 and e);(no X between e1 and e)) supposing (loc(e) = loc(e1)) \mwedge{} (loc(e1) = lo\000Cc(start))
Date html generated:
2016_05_16-PM-02_01_42
Last ObjectModification:
2016_01_17-PM-07_43_43
Theory : event-ordering
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