Nuprl Lemma : real-vec-mul_wf
∀[n:ℕ]. ∀[X:ℝ^n]. ∀[a:ℝ]. (a*X ∈ ℝ^n)
Proof
Definitions occuring in Statement :
real-vec-mul: a*X,
real-vec: ℝ^n,
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-mul: a*X,
nat: ℕ
Lemmas referenced :
rmul_wf,
int_seg_wf,
real_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[X:\mBbbR{}\^{}n]. \mforall{}[a:\mBbbR{}]. (a*X \mmember{} \mBbbR{}\^{}n)
Date html generated:
2016_05_18-AM-09_46_40
Last ObjectModification:
2015_12_27-PM-11_14_06
Theory : reals
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