Nuprl Lemma : real-vec-mul-linear-sub
∀[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-sub: 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-sub: X - Y,
req-vec: req-vec(n;x;y),
all: ∀x:A. B[x],
real-vec: ℝ^n,
and: P ∧ Q,
nat: ℕ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q
Lemmas referenced :
rmul-rsub-distrib,
int_seg_wf,
req_witness,
real-vec-mul_wf,
real-vec-sub_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,
productElimination,
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_36
Last ObjectModification:
2016_09_28-PM-00_38_49
Theory : reals
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