Nuprl Lemma : arctan-is-arctangent
∀[x:ℝ]. (arctan(x) = arctangent(x))
Proof
Definitions occuring in Statement :
arctan: arctan(x),
arctangent: arctangent(x),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
sq_stable: SqStable(P),
implies: P ⇒ Q
Lemmas referenced :
arctan_wf1,
sq_stable__req,
arctangent_wf,
real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (arctan(x) = arctangent(x))
Date html generated:
2018_05_22-PM-03_07_23
Last ObjectModification:
2017_10_27-AM-01_04_35
Theory : reals_2
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