Nuprl Lemma : hyp-dist_wf
∀[rv:InnerProductSpace]. ∀[x,y:Point]. (hyp (x,y) ∈ ℝ)
Proof
Definitions occuring in Statement :
hyp-dist: hyp (x,y),
inner-product-space: InnerProductSpace,
real: ℝ,
ss-point: Point,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hyp-dist: hyp (x,y),
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ
Lemmas referenced :
inv-cosh_wf,
ss-point_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
rsub_wf,
rmul_wf,
rsqrt_wf,
radd-non-neg,
int-to-real_wf,
rv-ip_wf,
rleq-int,
false_wf,
rv-ip-nonneg,
radd_wf,
rleq_wf,
real_wf,
req_wf,
hyp-distance-lemma1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
isect_memberEquality,
because_Cache,
dependent_set_memberEquality,
dependent_functionElimination,
natural_numberEquality,
independent_functionElimination,
productElimination,
independent_pairFormation,
lambdaFormation,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x,y:Point]. (hyp (x,y) \mmember{} \mBbbR{})
Date html generated:
2017_10_05-AM-00_29_14
Last ObjectModification:
2017_06_23-PM-05_52_55
Theory : inner!product!spaces
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