Nuprl Lemma : rnexp2-positive-iff
∀x:ℝ. (r0 < x^2 ⇐⇒ x ≠ r0)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rless: x < y,
rnexp: x^k1,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
false: False,
prop: ℙ,
rev_implies: P ⇐ Q,
nat_plus: ℕ+,
rless: x < y,
sq_exists: ∃x:A [B[x]],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Latex:
\mforall{}x:\mBbbR{}. (r0 < x\^{}2 \mLeftarrow{}{}\mRightarrow{} x \mneq{} r0)
Date html generated:
2020_05_20-AM-11_07_56
Last ObjectModification:
2020_01_06-PM-00_26_12
Theory : reals
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