Nuprl Lemma : rnexp-even-nonneg
∀n:ℕ. (((n rem 2) = 0 ∈ ℤ) ⇒ (∀x:ℝ. (r0 ≤ x^n)))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rnexp: x^k1,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
remainder: n rem m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
guard: {T},
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
and: P ∧ Q,
uiff: uiff(P;Q),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
prop: ℙ,
false: False,
not: ¬A,
nequal: a ≠ b ∈ T ,
true: True,
int_nzero: ℤ-o,
le: A ≤ B,
less_than': less_than'(a;b),
nat_plus: ℕ+,
rev_uimplies: rev_uimplies(P;Q)
Latex:
\mforall{}n:\mBbbN{}. (((n rem 2) = 0) {}\mRightarrow{} (\mforall{}x:\mBbbR{}. (r0 \mleq{} x\^{}n)))
Date html generated:
2020_05_20-AM-10_59_13
Last ObjectModification:
2020_01_03-AM-11_17_33
Theory : reals
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