Nuprl Lemma : fastpi_wf
∀n:ℕ. (fastpi(n) ∈ ℝ)
Proof
Definitions occuring in Statement :
fastpi: fastpi(n),
real: ℝ,
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
bfalse: ff,
ifthenelse: if b then t else f fi ,
assert: ↑b,
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
real: ℝ,
subtract: n - m,
primrec: primrec(n;b;c),
squash: ↓T,
less_than: a < b,
less_than': less_than'(a;b),
le: A ≤ B,
guard: {T},
sq_type: SQType(T),
nequal: a ≠ b ∈ T ,
true: True,
subtype_rel: A ⊆r B,
int-to-real: r(n),
nat_plus: ℕ+,
has-value: (a)↓,
exp: i^n,
int-rdiv: (a)/k1,
rational-approx: (x within 1/n),
fastpi: fastpi(n),
or: P ∨ Q,
decidable: Dec(P),
prop: ℙ,
and: P ∧ Q,
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
uimplies: b supposing a,
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
exp_wf_nat_plus,
mul_nat_plus,
rcos_wf,
radd_wf,
req_wf,
real_wf,
radd_rcos_wf,
multiply_nat_wf,
subtract-add-cancel,
exp_wf4,
mul_bounds_1a,
exp-fastexp,
iff_wf,
assert_wf,
assert_of_lt_int,
bfalse_wf,
lt_int_wf,
iff_imp_equal_bool,
bool_subtype_base,
bool_wf,
primrec-unroll,
iff_weakening_equal,
subtype_rel_self,
squash_wf,
regular-int-seq_wf,
le_wf,
false_wf,
exp_wf2,
half-pi_wf,
rational-approx_wf,
true_wf,
equal-wf-base,
int_subtype_base,
subtype_base_sq,
mul-commutes,
mul-associates,
int-value-type,
value-type-has-value,
nat_plus_wf,
primrec0_lemma,
nat_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
full-omega-unsat,
nat_properties
Rules used in proof :
setEquality,
addEquality,
impliesFunctionality,
productElimination,
universeEquality,
functionEquality,
imageElimination,
applyLambdaEquality,
imageMemberEquality,
dependent_set_memberEquality,
baseClosed,
cumulativity,
instantiate,
addLevel,
divideEquality,
applyEquality,
because_Cache,
multiplyEquality,
callbyvalueReduce,
computeAll,
functionExtensionality,
unionElimination,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_pairFormation,
sqequalRule,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
natural_numberEquality,
intWeakElimination,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}n:\mBbbN{}. (fastpi(n) \mmember{} \mBbbR{})
Date html generated:
2018_05_22-PM-02_58_57
Last ObjectModification:
2018_05_20-PM-11_04_00
Theory : reals_2
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