Nuprl Lemma : rtan-arctangent
∀[x:ℝ]. (rtan(arctangent(x)) = x)
Proof
Definitions occuring in Statement :
arctangent: arctangent(x),
rtan: rtan(x),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
top: Top,
and: P ∧ Q,
cand: A c∧ B,
i-member: r ∈ I,
rooint: (l, u),
implies: P ⇒ Q
Lemmas referenced :
arctangent-bounds,
arctangent_one_one,
rtan_wf,
arctangent_wf,
i-member_wf,
rooint_wf,
rminus_wf,
halfpi_wf,
arctangent-rtan,
req_witness,
member_rooint_lemma,
rless_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
isectElimination,
hypothesis,
because_Cache,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairFormation,
productEquality,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (rtan(arctangent(x)) = x)
Date html generated:
2018_05_22-PM-03_03_08
Last ObjectModification:
2017_10_22-AM-00_29_54
Theory : reals_2
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