Nuprl Lemma : eo-forward-before
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[e,b:E]. before(e) = filter(λa.b ≤loc a;before(e)) ∈ (E List) supposing b ≤loc e
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-before: before(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,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
nat: ℕ,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-le: e ≤loc e' ,
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e,b:E].
before(e) = filter(\mlambda{}a.b \mleq{}loc a;before(e)) supposing b \mleq{}loc e
Date html generated:
2016_05_16-PM-01_11_06
Last ObjectModification:
2016_01_17-PM-08_02_19
Theory : event-ordering
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