Nuprl Lemma : real-vec-dist-nonneg
∀[n:ℕ]. ∀[x,y:ℝ^n]. (r0 ≤ d(x;y))
Proof
Definitions occuring in Statement :
real-vec-dist: d(x;y),
real-vec: ℝ^n,
rleq: x ≤ y,
int-to-real: r(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False,
subtype_rel: A ⊆r B,
real: ℝ
Lemmas referenced :
real-vec-dist_wf,
set_wf,
real_wf,
rleq_wf,
int-to-real_wf,
sq_stable__rleq,
equal_wf,
less_than'_wf,
rsub_wf,
nat_plus_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
natural_numberEquality,
lambdaFormation,
setElimination,
rename,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setEquality,
minusEquality,
axiomEquality,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[x,y:\mBbbR{}\^{}n]. (r0 \mleq{} d(x;y))
Date html generated:
2016_10_26-AM-10_24_48
Last ObjectModification:
2016_09_25-AM-00_57_49
Theory : reals
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