Nuprl Lemma : eo-forward-E-subtype2
∀[Info:Type]. ∀[eo:EO+(Info)]. ∀[e:E]. ({e':E| (loc(e') = loc(e) ∈ Id) ⇒ e ≤loc e' } ⊆r E)
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
es-E: E,
es-base-E: es-base-E(es),
es-dom: es-dom(es),
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
and: P ∧ Q,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
not: ¬A,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
band: p ∧b q,
bfalse: ff,
exists: ∃x:A. B[x],
bnot: ¬bb,
false: False
Latex:
\mforall{}[Info:Type]. \mforall{}[eo:EO+(Info)]. \mforall{}[e:E]. (\{e':E| (loc(e') = loc(e)) {}\mRightarrow{} e \mleq{}loc e' \} \msubseteq{}r E)
Date html generated:
2016_05_16-PM-01_04_31
Last ObjectModification:
2015_12_29-PM-01_49_45
Theory : event-ordering
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