Nuprl Lemma : iter-arcsine-contraction_wf
∀[a:{a:ℝ| (r(-1) < a) ∧ (a < r1)} ]. ∀[n:ℕ]. (arcsine-contraction^n(a) ∈ ℝ)
Proof
Definitions occuring in Statement :
iter-arcsine-contraction: arcsine-contraction^n(a),
rless: x < y,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
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,
iter-arcsine-contraction: arcsine-contraction^n(a),
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
arcsine-contraction_wf,
rless_wf,
int-to-real_wf,
real_wf,
fun_exp_wf,
nat_wf,
set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
sqequalHypSubstitution,
productElimination,
lambdaEquality,
extract_by_obid,
isectElimination,
dependent_set_memberEquality,
hypothesisEquality,
independent_pairFormation,
hypothesis,
productEquality,
minusEquality,
natural_numberEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a:\{a:\mBbbR{}| (r(-1) < a) \mwedge{} (a < r1)\} ]. \mforall{}[n:\mBbbN{}]. (arcsine-contraction\^{}n(a) \mmember{} \mBbbR{})
Date html generated:
2016_10_26-PM-00_45_57
Last ObjectModification:
2016_10_13-PM-08_21_17
Theory : reals_2
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