Nuprl Lemma : ip-ge_wf
∀[rv:InnerProductSpace]. ∀[a,b,c,d:Point]. (cd ≥ ab ∈ ℙ)
Proof
Definitions occuring in Statement :
ip-ge: cd ≥ ab,
inner-product-space: InnerProductSpace,
ss-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ip-ge: cd ≥ ab,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
not_wf,
exists_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,
ip-between_wf,
ip-congruent_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
lambdaEquality,
because_Cache,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,c,d:Point]. (cd \mgeq{} ab \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-00_02_20
Last ObjectModification:
2017_03_19-PM-00_39_54
Theory : inner!product!spaces
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