Nuprl Lemma : rcos-shift-pi
∀[x:ℝ]. (rcos(x + π) = -(rcos(x)))
Proof
Definitions occuring in Statement :
pi: π,
rcos: rcos(x),
req: x = y,
rminus: -(x),
radd: a + b,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
pi: π,
implies: P ⇒ Q,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rcos_wf,
radd_wf,
pi_wf,
rminus_wf,
real_wf,
int-rmul_wf,
halfpi_wf,
rmul_wf,
int-to-real_wf,
req_wf,
req_weakening,
rsin_wf,
req_functionality,
radd_functionality,
int-rmul-req,
uiff_transitivity,
rmul_comm,
req_inversion,
radd-assoc,
radd_comm,
req_transitivity,
radd-ac,
rmul-identity1,
rmul-distrib2,
rmul_functionality,
radd-int,
rcos_functionality,
rcos-shift-half-pi,
rminus_functionality,
rsin-shift-half-pi
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
natural_numberEquality,
because_Cache,
addEquality,
independent_isectElimination,
productElimination,
sqequalRule
Latex:
\mforall{}[x:\mBbbR{}]. (rcos(x + \mpi{}) = -(rcos(x)))
Date html generated:
2016_10_26-PM-00_23_48
Last ObjectModification:
2016_09_12-PM-05_43_16
Theory : reals_2
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