Nuprl Lemma : ratreal-ratLegendre
∀[x:ℤ × ℕ+]. ∀[n:ℕ]. (ratreal(ratLegendre(n;x)) = Legendre(n;ratreal(x)))
Proof
Definitions occuring in Statement :
ratLegendre: ratLegendre(n;x),
Legendre: Legendre(n;x),
ratreal: ratreal(r),
req: x = y,
nat_plus: ℕ+,
nat: ℕ,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
ratLegendre_wf,
sq_stable__req,
ratreal_wf,
Legendre_wf,
req_witness,
istype-nat,
istype-int,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
lambdaFormation_alt,
setElimination,
rename,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
applyEquality,
lambdaEquality_alt,
isect_memberEquality_alt,
because_Cache,
isectIsTypeImplies,
productIsType,
universeIsType
Latex:
\mforall{}[x:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbN{}]. (ratreal(ratLegendre(n;x)) = Legendre(n;ratreal(x)))
Date html generated:
2019_10_30-AM-11_34_16
Last ObjectModification:
2019_01_14-AM-10_25_05
Theory : reals_2
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