Nuprl Lemma : rnexp-rless-odd
∀n:ℕ+. ((↑isOdd(n)) ⇒ (∀x,y:ℝ. ((x < y) ⇒ (x^n < y^n))))
Proof
Definitions occuring in Statement :
rless: x < y,
rnexp: x^k1,
real: ℝ,
isOdd: isOdd(n),
nat_plus: ℕ+,
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
prop: ℙ,
nat_plus: ℕ+,
uimplies: b supposing a,
itermConstant: "const",
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A,
top: Top,
uiff: uiff(P;Q),
and: P ∧ Q,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
iff: P ⇐⇒ Q
Lemmas referenced :
rless-cases1,
int-to-real_wf,
rless_wf,
real_wf,
assert_wf,
isOdd_wf,
nat_plus_wf,
rnexp-rless2,
rminus_wf,
rless-implies-rless,
real_term_polynomial,
itermSubtract_wf,
itermVar_wf,
itermMinus_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma,
req-iff-rsub-is-0,
rsub_wf,
itermConstant_wf,
rnexp_wf,
nat_plus_subtype_nat,
ifthenelse_wf,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
rless_functionality,
rnexp-rminus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
isectElimination,
natural_numberEquality,
unionElimination,
setElimination,
rename,
because_Cache,
independent_isectElimination,
sqequalRule,
computeAll,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
applyEquality,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid
Latex:
\mforall{}n:\mBbbN{}\msupplus{}. ((\muparrow{}isOdd(n)) {}\mRightarrow{} (\mforall{}x,y:\mBbbR{}. ((x < y) {}\mRightarrow{} (x\^{}n < y\^{}n))))
Date html generated:
2017_10_03-AM-08_40_09
Last ObjectModification:
2017_07_28-AM-07_31_12
Theory : reals
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