Nuprl Lemma : rabs-rmul-rleq
∀[x,y,a,b:ℝ]. (|x * y| ≤ (a * b)) supposing ((|y| ≤ b) and (|x| ≤ a))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rabs: |x|,
rmul: a * b,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
guard: {T},
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
prop: ℙ,
uiff: uiff(P;Q),
or: P ∨ Q,
cand: A c∧ B,
req_int_terms: t1 ≡ t2,
false: False,
implies: P ⇒ Q,
not: ¬A
Latex:
\mforall{}[x,y,a,b:\mBbbR{}]. (|x * y| \mleq{} (a * b)) supposing ((|y| \mleq{} b) and (|x| \mleq{} a))
Date html generated:
2020_05_20-AM-10_57_56
Last ObjectModification:
2020_01_06-PM-00_26_57
Theory : reals
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