Nuprl Lemma : list-eo-first
∀L:Top List. ∀i:Id. ∀a:ℕ||L||. (first(a) ~ (a =z 0))
Proof
Definitions occuring in Statement :
list-eo: list-eo(L;i),
es-first: first(e),
Id: Id,
length: ||as||,
list: T List,
int_seg: {i..j-},
eq_int: (i =z j),
top: Top,
all: ∀x:A. B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
es-first: first(e),
es-dom: es-dom(es),
es-pred: pred(e),
list-eo: list-eo(L;i),
let: let,
mk-extended-eo: mk-extended-eo,
member: t ∈ T,
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mk-eo: mk-eo(E;dom;l;R;locless;pred;rank),
mk-eo-record: mk-eo-record(E;dom;l;R;locless;pred;rank),
btrue: tt,
es-base-pred: pred1(e),
es-eq: es-eq(es),
es-eq-E: e = e',
es-locless: es-locless(es;e1;e2),
es-loc: loc(e),
infix_ap: x f y,
uall: ∀[x:A]. B[x],
int_seg: {i..j-},
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
lt_int: i <z j,
band: p ∧b q,
bor: p ∨bq,
not: ¬A,
iff: P ⇐⇒ Q,
nequal: a ≠ b ∈ T ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T
Latex:
\mforall{}L:Top List. \mforall{}i:Id. \mforall{}a:\mBbbN{}||L||. (first(a) \msim{} (a =\msubz{} 0))
Date html generated:
2016_05_17-AM-08_22_59
Last ObjectModification:
2016_01_17-PM-02_36_11
Theory : event-ordering
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