Nuprl Lemma : sq_stable__rv-sep
∀rv:InnerProductSpace. ∀x,y:Point. SqStable(x # y)
Proof
Definitions occuring in Statement :
inner-product-space: InnerProductSpace,
ss-sep: x # y,
ss-point: Point,
sq_stable: SqStable(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
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,
rv-sep-iff-norm,
ss-sep_wf,
rless_wf,
int-to-real_wf,
rv-norm_wf,
rv-sub_wf,
real_wf,
rleq_wf,
req_wf,
rmul_wf,
rv-ip_wf,
squash_wf,
sq_stable__rless
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
independent_pairFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
natural_numberEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
imageElimination,
imageMemberEquality,
baseClosed
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}x,y:Point. SqStable(x \# y)
Date html generated:
2017_10_04-PM-11_51_46
Last ObjectModification:
2017_03_12-PM-09_49_43
Theory : inner!product!spaces
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