Nuprl Lemma : eo-forward-le-before
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e,b:E]. ≤loc(e) = filter(λa.b ≤loc a;≤loc(e)) ∈ (E List) supposing b ≤loc e
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le-before: ≤loc(e),
es-ble: e ≤loc e',
es-le: e ≤loc e' ,
es-E: E,
filter: filter(P;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
es-le-before: ≤loc(e),
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
ifthenelse: if b then t else f fi ,
squash: ↓T,
true: True,
guard: {T},
rev_implies: P ⇐ Q,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e,b:E]. \mleq{}loc(e) = filter(\mlambda{}a.b \mleq{}loc a;\mleq{}loc(e)) supposing b \mleq{}loc e
Date html generated:
2016_05_16-PM-01_11_18
Last ObjectModification:
2016_01_17-PM-07_55_41
Theory : event-ordering
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