Nuprl Lemma : es-le-linorder
∀es:EO. ∀i:Id. Linorder({e:E| loc(e) = i ∈ Id} ;a,b.a ≤loc b )
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
linorder: Linorder(T;x,y.R[x; y]),
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
linorder: Linorder(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
order: Order(T;x,y.R[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
guard: {T},
es-le: e ≤loc e' ,
or: P ∨ Q,
false: False
Latex:
\mforall{}es:EO. \mforall{}i:Id. Linorder(\{e:E| loc(e) = i\} ;a,b.a \mleq{}loc b )
Date html generated:
2016_05_16-AM-09_21_05
Last ObjectModification:
2015_12_28-PM-09_54_15
Theory : new!event-ordering
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