Nuprl Lemma : real-vec-mul-linear
∀[n:ℕ]. ∀[X,Y:ℝ^n]. ∀[a:ℝ].  req-vec(n;a*X + Y;a*X + a*Y)
Proof
Definitions occuring in Statement : 
real-vec-mul: a*X
, 
real-vec-add: X + Y
, 
req-vec: req-vec(n;x;y)
, 
real-vec: ℝ^n
, 
real: ℝ
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
real-vec-mul: a*X
, 
real-vec-add: X + Y
, 
req-vec: req-vec(n;x;y)
, 
all: ∀x:A. B[x]
, 
real-vec: ℝ^n
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
Lemmas referenced : 
rmul-distrib1, 
int_seg_wf, 
req_witness, 
real-vec-mul_wf, 
real-vec-add_wf, 
real-vec_wf, 
real_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lambdaFormation, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
natural_numberEquality, 
setElimination, 
rename, 
lambdaEquality, 
dependent_functionElimination, 
independent_functionElimination, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[X,Y:\mBbbR{}\^{}n].  \mforall{}[a:\mBbbR{}].    req-vec(n;a*X  +  Y;a*X  +  a*Y)
Date html generated:
2016_10_26-AM-10_16_25
Last ObjectModification:
2016_09_26-PM-11_10_34
Theory : reals
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