Nuprl Lemma : sq_stable__ip-congruent
∀[rv:InnerProductSpace]. ∀[a,b,c,d:Point]. SqStable(ab=cd)
Proof
Definitions occuring in Statement :
ip-congruent: ab=cd,
inner-product-space: InnerProductSpace,
ss-point: Point,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ip-congruent: ab=cd,
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
sq_stable__req,
rv-norm_wf,
rv-sub_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
rmul_wf,
rv-ip_wf,
req_witness,
inner-product-space_subtype,
squash_wf,
ip-congruent_wf,
ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination,
instantiate,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,c,d:Point]. SqStable(ab=cd)
Date html generated:
2017_10_04-PM-11_56_27
Last ObjectModification:
2017_03_14-PM-03_13_48
Theory : inner!product!spaces
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