Nuprl Lemma : rinv-positive
∀x:ℝ. ((r0 < x) ⇒ (r0 < rinv(x)))
Proof
Definitions occuring in Statement :
rless: x < y,
rinv: rinv(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
rneq: x ≠ y,
or: P ∨ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
rpositive: rpositive(x),
sq_exists: ∃x:A [B[x]],
rinv: rinv(x),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
rless: x < y,
real: ℝ,
sq_stable: SqStable(P),
squash: ↓T,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
has-value: (a)↓,
nat: ℕ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
less_than: a < b,
true: True,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
less_than': less_than'(a;b),
reg-seq-inv: reg-seq-inv(x),
rpositive2: rpositive2(x),
nequal: a ≠ b ∈ T ,
cand: A c∧ B,
int_nzero: ℤ-o,
ge: i ≥ j ,
absval: |i|,
reg-seq-adjust: reg-seq-adjust(n;x)
Latex:
\mforall{}x:\mBbbR{}. ((r0 < x) {}\mRightarrow{} (r0 < rinv(x)))
Date html generated:
2020_05_20-AM-10_57_21
Last ObjectModification:
2020_01_06-PM-00_27_50
Theory : reals
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