Nuprl Lemma : list-eo-before
∀L:Top List. ∀i:Id. ∀e:E. (before(e) ~ upto(e))
Proof
Definitions occuring in Statement :
list-eo: list-eo(L;i),
es-before: before(e),
es-E: E,
Id: Id,
upto: upto(n),
list: T List,
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
uiff: uiff(P;Q),
and: P ∧ Q,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
prop: ℙ,
es-before: before(e),
lelt: i ≤ j < k,
le: A ≤ B,
less_than': less_than'(a;b),
eq_int: (i =z j),
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bool: 𝔹,
unit: Unit,
it: ⋅,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
squash: ↓T,
less_than: a < b,
subtype_rel: A ⊆r B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}L:Top List. \mforall{}i:Id. \mforall{}e:E. (before(e) \msim{} upto(e))
Date html generated:
2016_05_17-AM-08_23_40
Last ObjectModification:
2016_01_17-PM-02_41_54
Theory : event-ordering
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