Nuprl Lemma : uniform-fps_wf
∀[n:ℕ+]. (uniform-fps(n) ∈ FinProbSpace)
Proof
Definitions occuring in Statement :
uniform-fps: uniform-fps(n),
finite-prob-space: FinProbSpace,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uniform-fps: uniform-fps(n),
finite-prob-space: FinProbSpace,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_nzero: ℤ-o,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
qdiv: (r/s),
qmul: r * s,
callbyvalueall: callbyvalueall,
evalall: evalall(t),
qinv: 1/r,
l_all: (∀x∈L.P[x]),
nat: ℕ,
uiff: uiff(P;Q)
Lemmas referenced :
map_wf,
qdiv_wf,
int_nzero-rational,
subtype_rel_sets,
less_than_wf,
nequal_wf,
nat_plus_properties,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
map-length,
length_upto,
equal-wf-T-base,
qsum_wf,
select_wf,
decidable__le,
intformnot_wf,
intformle_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
decidable__lt,
length_wf,
rationals_wf,
l_all_wf2,
l_member_wf,
qle_wf,
nat_plus_wf,
equal_wf,
squash_wf,
true_wf,
qsum-const,
nat_plus_subtype_nat,
subtype_rel_set,
int-subtype-rationals,
iff_weakening_equal,
qmul-qdiv-cancel,
int_seg_wf,
select-map,
upto_wf,
subtype_rel_list,
top_wf,
lelt_wf,
map_length_nat,
nat_wf,
qinv-nonneg,
qless-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_set_memberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
lambdaEquality,
independent_isectElimination,
hypothesisEquality,
applyEquality,
intEquality,
natural_numberEquality,
hypothesis,
setElimination,
rename,
setEquality,
lambdaFormation,
applyLambdaEquality,
equalityTransitivity,
equalitySymmetry,
productElimination,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
baseClosed,
independent_functionElimination,
productEquality,
unionElimination,
imageElimination,
axiomEquality,
universeEquality,
imageMemberEquality,
hyp_replacement
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. (uniform-fps(n) \mmember{} FinProbSpace)
Date html generated:
2018_05_22-AM-00_33_27
Last ObjectModification:
2017_07_26-PM-06_59_44
Theory : randomness
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