Nuprl Lemma : es-le-linorder-interface
∀[Info:Type]. ∀es:EO+(Info). ∀X:EClass(Top). ∀j:Id. Linorder({e':E(X)| loc(e') = j ∈ Id} ;a,b.a ≤loc b )
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
Id: Id,
linorder: Linorder(T;x,y.R[x; y]),
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
linorder: Linorder(T;x,y.R[x; y]),
and: P ∧ Q,
order: Order(T;x,y.R[x; y]),
cand: A c∧ B,
refl: Refl(T;x,y.E[x; y]),
so_lambda: λ2x.t[x],
es-E-interface: E(X),
so_apply: x[s],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
connex: Connex(T;x,y.R[x; y]),
guard: {T},
anti_sym: AntiSym(T;x,y.R[x; y]),
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X:EClass(Top). \mforall{}j:Id. Linorder(\{e':E(X)| loc(e') = j\} ;a,b.a \mleq{}loc b )
Date html generated:
2016_05_16-PM-02_45_08
Last ObjectModification:
2016_01_17-PM-07_40_02
Theory : event-ordering
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