Nuprl Lemma : ip-between-trivial
∀[rv:InnerProductSpace]. ∀[a,b:Point]. b_b_a
Proof
Definitions occuring in Statement :
ip-between: a_b_c,
inner-product-space: InnerProductSpace,
ss-point: Point,
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,
implies: P ⇒ Q,
guard: {T},
uimplies: b supposing a,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
prop: ℙ
Lemmas referenced :
req_witness,
radd_wf,
rmul_wf,
rv-norm_wf,
rv-sub_wf,
inner-product-space_subtype,
rv-ip_wf,
int-to-real_wf,
ss-point_wf,
real-vector-space_subtype1,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
req_wf,
rv-0_wf,
uiff_transitivity,
req_functionality,
radd_functionality,
rv-ip_functionality,
rv-sub-same,
ss-eq_weakening,
rmul_functionality,
rv-norm_functionality,
req_weakening,
rv-0ip,
rv-norm0,
real_wf,
rleq_wf,
rmul-zero-both,
radd-zero-both
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
natural_numberEquality,
independent_functionElimination,
instantiate,
independent_isectElimination,
isect_memberEquality,
dependent_functionElimination,
productElimination,
lambdaEquality,
setElimination,
rename,
setEquality,
productEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[a,b:Point]. b\_b\_a
Date html generated:
2017_10_04-PM-11_59_44
Last ObjectModification:
2017_03_09-PM-05_43_31
Theory : inner!product!spaces
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