Nuprl Lemma : rabs-rleq
∀x,z:ℝ. (|x| ≤ z ⇐⇒ (-(z) ≤ x) ∧ (x ≤ z))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rabs: |x|,
rminus: -(x),
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
req_int_terms: t1 ≡ t2,
false: False,
not: ¬A
Latex:
\mforall{}x,z:\mBbbR{}. (|x| \mleq{} z \mLeftarrow{}{}\mRightarrow{} (-(z) \mleq{} x) \mwedge{} (x \mleq{} z))
Date html generated:
2020_05_20-AM-11_02_01
Last ObjectModification:
2019_12_12-AM-10_28_13
Theory : reals
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