Nuprl Lemma : iseg-filter-es-interval
∀[es:EO]. ∀[L:E List]. ∀[e1,e2:E]. ∀[P:{x:E| (x ∈ [e1, e2])} ⟶ 𝔹].
(L = filter(P;[e1, last(L)]) ∈ (E List)) supposing ((¬↑null(L)) and L ≤ filter(P;[e1, e2]))
Proof
Definitions occuring in Statement :
es-interval: [e, e'],
es-E: E,
event_ordering: EO,
iseg: l1 ≤ l2,
last: last(L),
l_member: (x ∈ l),
null: null(as),
filter: filter(P;l),
list: T List,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
not: ¬A,
false: False,
guard: {T},
rev_implies: P ⇐ Q,
cand: A c∧ B,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
or: P ∨ Q,
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
irrefl: Irrefl(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y])
Latex:
\mforall{}[es:EO]. \mforall{}[L:E List]. \mforall{}[e1,e2:E]. \mforall{}[P:\{x:E| (x \mmember{} [e1, e2])\} {}\mrightarrow{} \mBbbB{}].
(L = filter(P;[e1, last(L)])) supposing ((\mneg{}\muparrow{}null(L)) and L \mleq{} filter(P;[e1, e2]))
Date html generated:
2016_05_16-AM-09_38_49
Last ObjectModification:
2015_12_28-PM-09_58_05
Theory : new!event-ordering
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