Nuprl Lemma : ip-congruent-trans
∀[rv:InnerProductSpace]. ∀[a,b,p,q,r,s:Point]. (pq=rs) supposing (ab=rs and ab=pq)
Proof
Definitions occuring in Statement :
ip-congruent: ab=cd,
inner-product-space: InnerProductSpace,
ss-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
ip-congruent: ab=cd,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
req_inversion,
rv-norm_wf,
rv-sub_wf,
inner-product-space_subtype,
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
rmul_wf,
rv-ip_wf,
req_transitivity,
req_witness,
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,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
natural_numberEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
instantiate
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,p,q,r,s:Point]. (pq=rs) supposing (ab=rs and ab=pq)
Date html generated:
2017_10_04-PM-11_56_34
Last ObjectModification:
2017_03_09-PM-07_07_59
Theory : inner!product!spaces
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