Nuprl Lemma : fps-not-null
∀[p:FinProbSpace]. (null(p) ~ ff)
Proof
Definitions occuring in Statement :
finite-prob-space: FinProbSpace,
null: null(as),
bfalse: ff,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
finite-prob-space: FinProbSpace,
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
false: False,
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,
lt_int: i <z j,
length: ||as||,
list_ind: list_ind,
nil: [],
it: ⋅,
grp_id: e,
pi1: fst(t),
pi2: snd(t),
add_grp_of_rng: r↓+gp,
rng_zero: 0,
qrng: <ℚ+*>,
eq_int: (i =z j),
rev_implies: P ⇐ Q,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
sq_type: SQType(T),
cons: [a / b],
top: Top
Lemmas referenced :
rationals_wf,
list-cases,
null_nil_lemma,
subtype_base_sq,
bool_wf,
bool_subtype_base,
equal_wf,
squash_wf,
true_wf,
btrue_wf,
ppcc-problem,
unit_wf2,
iff_imp_equal_bool,
bfalse_wf,
assert-qeq,
false_wf,
iff_weakening_equal,
product_subtype_list,
null_cons_lemma,
finite-prob-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
hypothesis,
isectElimination,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
instantiate,
cumulativity,
independent_isectElimination,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
because_Cache,
unionEquality,
inlEquality,
independent_pairFormation,
lambdaFormation,
voidElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
sqequalAxiom
Latex:
\mforall{}[p:FinProbSpace]. (null(p) \msim{} ff)
Date html generated:
2018_05_22-AM-00_33_22
Last ObjectModification:
2017_07_26-PM-06_59_44
Theory : randomness
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