Nuprl Lemma : binary-fps_wf
*50/50* ∈ FinProbSpace
Proof
Definitions occuring in Statement :
binary-fps: *50/50*,
finite-prob-space: FinProbSpace,
member: t ∈ T
Definitions unfolded in proof :
binary-fps: *50/50*,
finite-prob-space: FinProbSpace,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
int_seg: {i..j-},
top: Top,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
so_apply: x[s],
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(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,
length: ||as||,
list_ind: list_ind,
cons: [a / b],
nil: [],
it: ⋅,
btrue: tt,
infix_ap: x f y,
grp_op: *,
pi1: fst(t),
pi2: snd(t),
add_grp_of_rng: r↓+gp,
rng_plus: +r,
qrng: <ℚ+*>,
qadd: r + s,
subtract: n - m,
bfalse: ff,
grp_id: e,
rng_zero: 0,
select: L[n],
qdiv: (r/s),
qmul: r * s,
qinv: 1/r,
eq_int: (i =z j),
assert: ↑b,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
qle: r ≤ s,
grp_leq: a ≤ b,
grp_le: ≤b,
qadd_grp: <ℚ+>,
q_le: q_le(r;s),
bor: p ∨bq,
qpositive: qpositive(r),
qsub: r - s,
band: p ∧b q,
less_than: a < b,
squash: ↓T
Lemmas referenced :
l_member_wf,
l_all_wf2,
equal-wf-T-base,
l_all_single,
qle_wf,
l_all_cons,
int_seg_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
length_of_nil_lemma,
length_of_cons_lemma,
nil_wf,
rationals_wf,
select_wf,
nequal_wf,
true_wf,
equal_wf,
int_subtype_base,
subtype_base_sq,
int_nzero-rational,
qdiv_wf,
cons_wf,
length_wf,
qsum_wf,
assert-qeq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
because_Cache,
independent_isectElimination,
dependent_set_memberEquality,
addLevel,
lambdaFormation,
instantiate,
cumulativity,
intEquality,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
hypothesisEquality,
introduction,
sqequalRule,
lambdaEquality,
applyEquality,
setElimination,
rename,
isect_memberEquality,
voidEquality,
addEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
setEquality,
baseClosed,
productEquality,
imageElimination
Latex:
*50/50* \mmember{} FinProbSpace
Date html generated:
2016_05_15-PM-11_44_48
Last ObjectModification:
2016_01_17-AM-10_07_47
Theory : randomness
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