Nuprl Lemma : real-vec-sub_wf
∀[n:ℕ]. ∀[X,Y:ℝ^n]. (X - Y ∈ ℝ^n)
Proof
Definitions occuring in Statement :
real-vec-sub: X - Y,
real-vec: ℝ^n,
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-sub: X - Y,
nat: ℕ
Lemmas referenced :
rsub_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,
applyEquality,
hypothesisEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[X,Y:\mBbbR{}\^{}n]. (X - Y \mmember{} \mBbbR{}\^{}n)
Date html generated:
2016_05_18-AM-09_46_01
Last ObjectModification:
2015_12_27-PM-11_14_57
Theory : reals
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