### 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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