Nuprl Lemma : sq_stable__real-vec-sep
∀n:ℕ. ∀a,b:ℝ^n. SqStable(a ≠ b)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
real-vec: ℝ^n,
nat: ℕ,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
real-vec-sep: a ≠ b,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
sq_stable__rless,
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,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b:\mBbbR{}\^{}n. SqStable(a \mneq{} b)
Date html generated:
2017_10_03-AM-10_59_08
Last ObjectModification:
2017_08_11-PM-05_28_49
Theory : reals
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