Nuprl Lemma : sq_stable__ip-between
∀[rv:InnerProductSpace]. ∀[a,b,c:Point]. SqStable(a_b_c)
Proof
Definitions occuring in Statement :
ip-between: a_b_c,
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-between: a_b_c,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
sq_stable__req,
radd_wf,
rmul_wf,
rv-norm_wf,
rv-sub_wf,
inner-product-space_subtype,
rv-ip_wf,
int-to-real_wf,
req_witness,
squash_wf,
ip-between_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,
hypothesis,
sqequalRule,
because_Cache,
natural_numberEquality,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination,
instantiate,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,c:Point]. SqStable(a\_b\_c)
Date html generated:
2017_10_04-PM-11_59_54
Last ObjectModification:
2017_03_14-PM-03_14_57
Theory : inner!product!spaces
Home
Index