Nuprl Lemma : rmul-nonneg-rabs
∀[x,y:ℝ].  (x * |y|) = |x * y| supposing r0 ≤ x
Proof
Definitions occuring in Statement : 
rleq: x ≤ y
, 
rabs: |x|
, 
req: x = y
, 
rmul: a * b
, 
int-to-real: r(n)
, 
real: ℝ
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
natural_number: $n
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced : 
req_witness, 
rmul_wf, 
rabs_wf, 
rleq_wf, 
int-to-real_wf, 
real_wf, 
req_weakening, 
req_functionality, 
rabs-rmul, 
rmul_functionality, 
rabs-of-nonneg
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
universeIsType, 
natural_numberEquality, 
sqequalRule, 
isect_memberEquality_alt, 
because_Cache, 
isectIsTypeImplies, 
inhabitedIsType, 
independent_isectElimination, 
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}].    (x  *  |y|)  =  |x  *  y|  supposing  r0  \mleq{}  x
Date html generated:
2019_10_29-AM-09_39_09
Last ObjectModification:
2019_02_13-PM-02_32_11
Theory : reals
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