Nuprl Lemma : rless-arcsine
∀x:{x:ℝ| x ∈ (r(-1), r1)} . (-(π/2) < arcsine(x))
Proof
Definitions occuring in Statement :
arcsine: arcsine(x),
halfpi: π/2,
rooint: (l, u),
i-member: r ∈ I,
rless: x < y,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
arcsine-bounds,
member_rooint_lemma,
set_wf,
real_wf,
i-member_wf,
rooint_wf,
int-to-real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
productElimination,
isectElimination,
lambdaEquality,
minusEquality,
natural_numberEquality,
because_Cache
Latex:
\mforall{}x:\{x:\mBbbR{}| x \mmember{} (r(-1), r1)\} . (-(\mpi{}/2) < arcsine(x))
Date html generated:
2016_10_26-PM-00_42_22
Last ObjectModification:
2016_09_12-PM-05_46_02
Theory : reals_2
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