Nuprl Lemma : rabs-rcos-rleq
∀x:ℝ. (|rcos(x)| ≤ r1)
Proof
Definitions occuring in Statement :
rcos: rcos(x),
rleq: x ≤ y,
rabs: |x|,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
real_wf,
rabs_wf,
rcos_wf,
cosine_wf,
int-to-real_wf,
rabs-cosine-rleq,
rleq_functionality,
rabs_functionality,
rcos-is-cosine,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}x:\mBbbR{}. (|rcos(x)| \mleq{} r1)
Date html generated:
2016_10_26-PM-00_15_00
Last ObjectModification:
2016_09_12-PM-05_40_42
Theory : reals_2
Home
Index