Nuprl Lemma : arcsine_deriv_wf
∀[x:{x:ℝ| x ∈ (r(-1), r1)} ]. (arcsine_deriv(x) ∈ ℝ)
Proof
Definitions occuring in Statement :
arcsine_deriv: arcsine_deriv(x),
rooint: (l, u),
i-member: r ∈ I,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
i-member: r ∈ I,
rooint: (l, u),
and: P ∧ Q,
top: Top,
sq_stable: SqStable(P),
squash: ↓T,
arcsine_deriv: arcsine_deriv(x),
guard: {T},
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
rneq: x ≠ y,
or: P ∨ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
arcsine-root-bounds,
member_rooint_lemma,
sq_stable__rless,
int-to-real_wf,
rdiv_wf,
rsqrt_wf,
rleq_weakening_rless,
rsub_wf,
rmul_wf,
rleq_wf,
rsqrt-positive,
rless_wf,
set_wf,
real_wf,
i-member_wf,
rooint_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
independent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
isectElimination,
minusEquality,
natural_numberEquality,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
because_Cache,
independent_isectElimination,
dependent_set_memberEquality,
applyEquality,
inrFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaEquality
Latex:
\mforall{}[x:\{x:\mBbbR{}| x \mmember{} (r(-1), r1)\} ]. (arcsine\_deriv(x) \mmember{} \mBbbR{})
Date html generated:
2016_10_26-PM-00_41_06
Last ObjectModification:
2016_09_12-PM-05_45_23
Theory : reals_2
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