Nuprl Lemma : rabs-ub
∀a:ℝ. ((r0 < a) ⇒ (∀x:ℝ. (a ≤ |x| ⇐⇒ (a ≤ x) ∨ (a ≤ -(x)))))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rless: x < y,
rabs: |x|,
rminus: -(x),
int-to-real: r(n),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
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,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
rless: x < y,
sq_exists: ∃x:A [B[x]],
false: False,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
less_than': less_than'(a;b),
true: True,
req_int_terms: t1 ≡ t2,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y
Latex:
\mforall{}a:\mBbbR{}. ((r0 < a) {}\mRightarrow{} (\mforall{}x:\mBbbR{}. (a \mleq{} |x| \mLeftarrow{}{}\mRightarrow{} (a \mleq{} x) \mvee{} (a \mleq{} -(x)))))
Date html generated:
2020_05_20-AM-11_02_52
Last ObjectModification:
2019_12_14-PM-00_54_52
Theory : reals
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