Nuprl Lemma : ip-triangle_wf
∀[rv:InnerProductSpace]. ∀[a,b,c:Point]. (Δ(a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
ip-triangle: Δ(a;b;c),
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-triangle: Δ(a;b;c),
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
rless_wf,
rabs_wf,
rv-ip_wf,
rv-sub_wf,
inner-product-space_subtype,
rmul_wf,
rv-norm_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_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,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
independent_isectElimination,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b,c:Point]. (\mDelta{}(a;b;c) \mmember{} \mBbbP{})
Date html generated:
2017_10_04-PM-11_57_55
Last ObjectModification:
2017_03_09-PM-02_04_42
Theory : inner!product!spaces
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