Nuprl Lemma : rnexp-is-positive
∀i:ℕ+. ∀x:ℝ. ((r0 < |x^i|) ⇒ (r0 < |x|))
Proof
Definitions occuring in Statement :
rless: x < y,
rabs: |x|,
rnexp: x^k1,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
false: False,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
prop: ℙ,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
rless: x < y,
sq_exists: ∃x:A [B[x]],
subtype_rel: A ⊆r B,
top: Top,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
rev_implies: P ⇐ Q,
bfalse: ff,
squash: ↓T,
less_than: a < b
Latex:
\mforall{}i:\mBbbN{}\msupplus{}. \mforall{}x:\mBbbR{}. ((r0 < |x\^{}i|) {}\mRightarrow{} (r0 < |x|))
Date html generated:
2020_05_20-AM-11_07_44
Last ObjectModification:
2019_12_14-PM-00_55_47
Theory : reals
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