Nuprl Lemma : alt-arcsin_wf
∀[a:{a:ℝ| a ∈ (r(-1), r1)} ]. (alt-arcsin(a) ∈ {y:ℝ| y = arcsine(a)} )
Proof
Definitions occuring in Statement :
alt-arcsin: alt-arcsin(a),
arcsine: arcsine(x),
rooint: (l, u),
i-member: r ∈ I,
req: x = y,
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,
alt-arcsin: alt-arcsin(a),
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
so_apply: x[s]
Lemmas referenced :
real-from-approx_wf,
arcsine_wf,
i-member_wf,
rooint_wf,
int-to-real_wf,
near-arcsine_wf,
nat_plus_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
setElimination,
thin,
rename,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
dependent_set_memberEquality_alt,
hypothesisEquality,
hypothesis,
universeIsType,
minusEquality,
natural_numberEquality,
lambdaEquality_alt,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
setIsType
Latex:
\mforall{}[a:\{a:\mBbbR{}| a \mmember{} (r(-1), r1)\} ]. (alt-arcsin(a) \mmember{} \{y:\mBbbR{}| y = arcsine(a)\} )
Date html generated:
2019_10_31-AM-06_14_03
Last ObjectModification:
2019_05_21-PM-11_17_23
Theory : reals_2
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