Nuprl Lemma : rcos-is-cosine
∀[x:ℝ]. (rcos(x) = cosine(x))
Proof
Definitions occuring in Statement :
rcos: rcos(x),
cosine: cosine(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,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
rcos_wf1,
sq_stable__req,
cosine_wf,
req_inversion,
real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
independent_isectElimination
Latex:
\mforall{}[x:\mBbbR{}]. (rcos(x) = cosine(x))
Date html generated:
2016_10_26-PM-00_14_28
Last ObjectModification:
2016_09_12-PM-05_40_19
Theory : reals_2
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