Nuprl Lemma : real-vec-sep_wf
∀[n:ℕ]. ∀[a,b:ℝ^n]. (a ≠ b ∈ ℙ)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec-sep: a ≠ b,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
rless_wf,
int-to-real_wf,
real-vec-dist_wf,
real_wf,
rleq_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbR{}\^{}n]. (a \mneq{} b \mmember{} \mBbbP{})
Date html generated:
2016_10_26-AM-10_29_15
Last ObjectModification:
2016_09_24-PM-10_58_07
Theory : reals
Home
Index