Nuprl Lemma : unit-fps_wf
*1* ∈ FinProbSpace
Proof
Definitions occuring in Statement :
unit-fps: *1*,
finite-prob-space: FinProbSpace,
member: t ∈ T
Definitions unfolded in proof :
unit-fps: *1*,
finite-prob-space: FinProbSpace,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
subtype_rel: A ⊆r B,
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],
eq_int: (i =z j),
assert: ↑b,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
less_than: a < b,
squash: ↓T
Lemmas referenced :
l_member_wf,
l_all_wf2,
equal-wf-T-base,
rationals_wf,
l_all_nil,
false_wf,
qle-int,
qle_wf,
l_all_cons,
int_seg_wf,
int-subtype-rationals,
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,
cons_wf,
select_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,
hypothesis,
sqequalRule,
lambdaEquality,
intEquality,
setElimination,
rename,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
addEquality,
productElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
lambdaFormation,
dependent_set_memberEquality,
productEquality,
imageElimination,
baseClosed,
setEquality
Latex:
*1* \mmember{} FinProbSpace
Date html generated:
2016_05_15-PM-11_44_45
Last ObjectModification:
2016_01_17-AM-10_07_40
Theory : randomness
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