Nuprl Lemma : near-arcsine-exists-ext
∀a:{a:ℝ| a ∈ (r(-1), r1)} . ∀N:ℕ+. (∃y:ℝ [(|y - arcsine(a)| ≤ (r1/r(N)))])
Proof
Definitions occuring in Statement :
arcsine: arcsine(x),
rooint: (l, u),
i-member: r ∈ I,
rdiv: (x/y),
rleq: x ≤ y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
sq_exists: ∃x:A [B[x]],
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
squash: ↓T,
or: P ∨ Q,
guard: {T},
prop: ℙ,
has-value: (a)↓,
implies: P ⇒ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
strict4: strict4(F),
uimplies: b supposing a,
top: Top,
so_apply: x[s1;s2;s3;s4],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
uall: ∀[x:A]. B[x],
sq_stable__rless,
by-nearby-cases-ext,
near-arcsine-exists,
int-rdiv: (a)/k1,
int-to-real: r(n),
bfalse: ff,
it: ⋅,
btrue: tt,
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
quick-find: quick-find(p;n),
rlessw: rlessw(x;y),
member: t ∈ T
Lemmas referenced :
lifting-strict-less,
is-exception_wf,
base_wf,
has-value_wf_base,
lifting-strict-callbyvalue,
near-arcsine-exists,
sq_stable__rless,
by-nearby-cases-ext
Rules used in proof :
because_Cache,
inlFormation,
imageElimination,
imageMemberEquality,
inrFormation,
applyExceptionCases,
hypothesisEquality,
closedConclusion,
baseApply,
callbyvalueApply,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
voidEquality,
voidElimination,
isect_memberEquality,
baseClosed,
isectElimination,
sqleReflexivity,
callbyvalueReduce,
equalitySymmetry,
equalityTransitivity,
sqequalHypSubstitution,
thin,
sqequalRule,
hypothesis,
extract_by_obid,
instantiate,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
introduction
Latex:
\mforall{}a:\{a:\mBbbR{}| a \mmember{} (r(-1), r1)\} . \mforall{}N:\mBbbN{}\msupplus{}. (\mexists{}y:\mBbbR{} [(|y - arcsine(a)| \mleq{} (r1/r(N)))])
Date html generated:
2018_05_22-PM-03_07_57
Last ObjectModification:
2018_05_20-PM-11_35_55
Theory : reals_2
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