Nuprl Lemma : rsin-rcos-pythag
∀x:ℝ. ((rsin(x)^2 + rcos(x)^2) = r1)
Proof
Definitions occuring in Statement :
rcos: rcos(x),
rsin: rsin(x),
rnexp: x^k1,
req: x = y,
radd: a + b,
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],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
real_wf,
radd_wf,
rnexp_wf,
false_wf,
le_wf,
rsin_wf,
rcos_wf,
sine_wf,
cosine_wf,
int-to-real_wf,
sine-cosine-pythag,
req_functionality,
radd_functionality,
rnexp_functionality,
rcos-is-cosine,
rsin-is-sine,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesisEquality,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
productElimination
Latex:
\mforall{}x:\mBbbR{}. ((rsin(x)\^{}2 + rcos(x)\^{}2) = r1)
Date html generated:
2016_10_26-PM-00_14_47
Last ObjectModification:
2016_09_12-PM-05_40_34
Theory : reals_2
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