Nuprl Lemma : ip-triangle-symmetry
∀rv:InnerProductSpace. ∀a,b,c:Point. (Δ(a;b;c) ⇒ Δ(c;b;a))
Proof
Definitions occuring in Statement :
ip-triangle: Δ(a;b;c),
inner-product-space: InnerProductSpace,
ss-point: Point,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
ip-triangle: Δ(a;b;c),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
and: P ∧ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
ip-triangle_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,
rmul_comm,
rv-norm_wf,
rv-sub_wf,
real_wf,
rleq_wf,
int-to-real_wf,
req_wf,
rmul_wf,
rv-ip_wf,
rabs_wf,
rless_functionality,
req_weakening,
rabs_functionality,
rv-ip-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
cut,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality,
natural_numberEquality,
dependent_functionElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}a,b,c:Point. (\mDelta{}(a;b;c) {}\mRightarrow{} \mDelta{}(c;b;a))
Date html generated:
2017_10_04-PM-11_58_06
Last ObjectModification:
2017_03_10-PM-01_16_18
Theory : inner!product!spaces
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