Nuprl Lemma : es-causl-max-list
∀es:EO. ∀L:E List. (0 < ||L|| ⇒ (¬(∀e:{e:E| (e ∈ L)} . ∃e':{e:E| (e ∈ L)} . (e < e'))))
Proof
Definitions occuring in Statement :
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
and: P ∧ Q,
subtype_rel: A ⊆r B,
guard: {T},
nat: ℕ,
int_seg: {i..j-},
uimplies: b supposing a,
ge: i ≥ j ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
cand: A c∧ B,
sorted-by: sorted-by(R;L),
select: L[n],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
le: A ≤ B,
less_than': less_than'(a;b),
length: ||as||,
list_ind: list_ind,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
iff: P ⇐⇒ Q,
cons: [a / b],
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
rev_implies: P ⇐ Q,
l_all: (∀x∈L.P[x]),
sq_stable: SqStable(P),
true: True,
es-E: E,
es-base-E: es-base-E(es),
l_contains: A ⊆ B
Latex:
\mforall{}es:EO. \mforall{}L:E List. (0 < ||L|| {}\mRightarrow{} (\mneg{}(\mforall{}e:\{e:E| (e \mmember{} L)\} . \mexists{}e':\{e:E| (e \mmember{} L)\} . (e < e'))))
Date html generated:
2016_05_16-AM-09_22_13
Last ObjectModification:
2016_01_17-PM-01_31_38
Theory : new!event-ordering
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