Nuprl Lemma : rcos-arccos
∀[a:{a:ℝ| a ∈ [r(-1), r1]} ]. (rcos(arccos(a)) = a)
Proof
Definitions occuring in Statement :
arccos: arccos(x),
rcos: rcos(x),
rccint: [l, u],
i-member: r ∈ I,
req: x = y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
set: {x:A| B[x]} ,
minus: -n,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
and: P ∧ Q,
sq_stable: SqStable(P),
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
arccos_wf,
sq_stable__req,
rcos_wf,
real_wf,
i-member_wf,
rccint_wf,
int-to-real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_functionElimination,
setIsType,
universeIsType,
minusEquality,
natural_numberEquality
Latex:
\mforall{}[a:\{a:\mBbbR{}| a \mmember{} [r(-1), r1]\} ]. (rcos(arccos(a)) = a)
Date html generated:
2019_10_31-AM-06_16_11
Last ObjectModification:
2019_05_23-AM-11_34_54
Theory : reals_2
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