Nuprl Lemma : pseudo-positive-iff
∀x:ℝ. ((r0 ≤ x) ⇒ (pseudo-positive(x) ⇐⇒ ∀y:ℝ. ((¬(x = y)) ∨ (¬(y = r0)))))
Proof
Definitions occuring in Statement :
pseudo-positive: pseudo-positive(x),
rleq: x ≤ y,
req: x = y,
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
not: ¬A,
false: False,
pseudo-positive: pseudo-positive(x),
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
cand: A c∧ B,
rless: x < y,
sq_exists: ∃x:A [B[x]],
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Latex:
\mforall{}x:\mBbbR{}. ((r0 \mleq{} x) {}\mRightarrow{} (pseudo-positive(x) \mLeftarrow{}{}\mRightarrow{} \mforall{}y:\mBbbR{}. ((\mneg{}(x = y)) \mvee{} (\mneg{}(y = r0)))))
Date html generated:
2020_05_20-AM-11_09_14
Last ObjectModification:
2020_01_09-PM-04_35_54
Theory : reals
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