Nuprl Lemma : Legendre-minus-1
∀n:ℕ. (Legendre(n;r(-1)) = r((-1)^n))
Proof
Definitions occuring in Statement :
Legendre: Legendre(n;x),
req: x = y,
int-to-real: r(n),
exp: i^n,
nat: ℕ,
all: ∀x:A. B[x],
minus: -n,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
true: True,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
squash: ↓T,
prop: ℙ,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top
Lemmas referenced :
istype-nat,
req_wf,
Legendre_wf,
int-to-real_wf,
exp_wf2,
rmul_wf,
rnexp_wf,
rminus_wf,
itermSubtract_wf,
itermMultiply_wf,
itermVar_wf,
itermConstant_wf,
req-iff-rsub-is-0,
uiff_transitivity,
uiff_transitivity3,
squash_wf,
true_wf,
real_wf,
rminus-int,
req_functionality,
Legendre-rminus,
req_weakening,
rmul_functionality,
Legendre-1,
rnexp_functionality,
rminus-as-rmul,
rnexp-rmul,
rnexp-int,
rnexp-one,
real_polynomial_null,
istype-int,
real_term_value_sub_lemma,
istype-void,
real_term_value_mul_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
minusEquality,
natural_numberEquality,
because_Cache,
productElimination,
independent_isectElimination,
sqequalRule,
independent_functionElimination,
applyEquality,
lambdaEquality_alt,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeIsType,
inhabitedIsType,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
approximateComputation,
int_eqEquality,
isect_memberEquality_alt,
voidElimination
Latex:
\mforall{}n:\mBbbN{}. (Legendre(n;r(-1)) = r((-1)\^{}n))
Date html generated:
2019_10_30-AM-11_33_39
Last ObjectModification:
2019_01_18-PM-08_36_45
Theory : reals_2
Home
Index