Nuprl Lemma : natural_number_wf_p-outcome
∀[p:FinProbSpace]. (0 ∈ Outcome)
Proof
Definitions occuring in Statement :
p-outcome: Outcome,
finite-prob-space: FinProbSpace,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
finite-prob-space: FinProbSpace,
all: ∀x:A. B[x],
or: P ∨ Q,
select: L[n],
uimplies: b supposing a,
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
uiff: uiff(P;Q),
qeq: qeq(r;s),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
qsum: Σa ≤ j < b. E[j],
rng_sum: rng_sum,
mon_itop: Π lb ≤ i < ub. E[i],
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
grp_id: e,
pi1: fst(t),
pi2: snd(t),
add_grp_of_rng: r↓+gp,
rng_zero: 0,
qrng: <ℚ+*>,
btrue: tt,
eq_int: (i =z j),
assert: ↑b,
cons: [a / b],
guard: {T},
nat: ℕ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
subtype_rel: A ⊆r B,
true: True,
p-outcome: Outcome,
int_seg: {i..j-}
Lemmas referenced :
false_wf,
rationals_wf,
list-cases,
length_of_nil_lemma,
stuck-spread,
base_wf,
assert-qeq,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__lt,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel,
equal_wf,
lelt_wf,
length_wf,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
extract_by_obid,
natural_numberEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
baseClosed,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
hypothesis_subsumption,
addEquality,
independent_functionElimination,
applyEquality,
lambdaEquality,
intEquality,
because_Cache,
minusEquality,
dependent_set_memberEquality,
axiomEquality
Latex:
\mforall{}[p:FinProbSpace]. (0 \mmember{} Outcome)
Date html generated:
2018_05_22-AM-00_33_30
Last ObjectModification:
2017_07_26-PM-06_59_45
Theory : randomness
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