Nuprl Lemma : arcsine-contraction_wf
∀[a:{a:ℝ| (r(-1) < a) ∧ (a < r1)} ]. ∀[x:ℝ]. (arcsine-contraction(a;x) ∈ ℝ)
Proof
Definitions occuring in Statement :
arcsine-contraction: arcsine-contraction(a;x),
rless: x < y,
int-to-real: r(n),
real: ℝ,
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,
arcsine-contraction: arcsine-contraction(a;x),
and: P ∧ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
guard: {T},
req_int_terms: t1 ≡ t2,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
radd_wf,
rsub_wf,
rmul_wf,
rcos_wf,
rsqrt_wf,
int-to-real_wf,
radd-preserves-rleq,
rleq_functionality,
radd-zero,
rleq_wf,
rsin_wf,
real_wf,
set_wf,
rless_wf,
itermSubtract_wf,
itermAdd_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
req-iff-rsub-is-0,
rnexp_wf,
false_wf,
le_wf,
rminus_wf,
rleq_weakening,
rless_transitivity2,
rleq_weakening_rless,
itermMinus_wf,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma,
iff_transitivity,
iff_weakening_uiff,
req_inversion,
rnexp2,
req_weakening,
square-rleq-1-iff,
rabs-rleq-iff,
real_term_value_minus_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
sqequalHypSubstitution,
productElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
because_Cache,
hypothesis,
dependent_set_memberEquality,
natural_numberEquality,
independent_isectElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
lambdaEquality,
productEquality,
minusEquality,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
approximateComputation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[a:\{a:\mBbbR{}| (r(-1) < a) \mwedge{} (a < r1)\} ]. \mforall{}[x:\mBbbR{}]. (arcsine-contraction(a;x) \mmember{} \mBbbR{})
Date html generated:
2019_10_31-AM-06_12_21
Last ObjectModification:
2018_08_23-AM-11_25_43
Theory : reals_2
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