Nuprl Lemma : es-le-before-partition
∀[es:EO]. ∀[e,a:E]. ≤loc(e) = (before(a) @ [a, e]) ∈ (E List) supposing a ≤loc e
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-le-before: ≤loc(e),
es-before: before(e),
es-le: e ≤loc e' ,
es-E: E,
event_ordering: EO,
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
es-le-before: ≤loc(e),
so_lambda: λ2x.t[x],
so_apply: x[s],
es-le: e ≤loc e' ,
or: P ∨ Q,
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
guard: {T},
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
top: Top,
squash: ↓T,
true: True,
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
Latex:
\mforall{}[es:EO]. \mforall{}[e,a:E]. \mleq{}loc(e) = (before(a) @ [a, e]) supposing a \mleq{}loc e
Date html generated:
2016_05_16-AM-09_34_37
Last ObjectModification:
2016_01_17-PM-01_28_38
Theory : new!event-ordering
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