Nuprl Lemma : rv-ip0
∀[rv:InnerProductSpace]. ∀[x:Point]. (x ⋅ 0 = r0)
Proof
Definitions occuring in Statement :
rv-ip: x ⋅ y,
inner-product-space: InnerProductSpace,
rv-0: 0,
ss-point: Point,
req: x = y,
int-to-real: r(n),
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rmul-one-both,
rmul-zero-both,
radd-int,
rmul_functionality,
rmul-distrib2,
rmul-identity1,
rminus-as-rmul,
radd_functionality,
req_transitivity,
uiff_transitivity,
req_inversion,
rmul_wf,
req_wf,
rminus_wf,
radd-preserves-req,
rv-ip-add2,
req_weakening,
ss-eq_inversion,
ss-eq_weakening,
rv-ip_functionality,
req_functionality,
radd_comm,
radd_wf,
rv-add_wf,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
real-vector-space_subtype1,
ss-point_wf,
int-to-real_wf,
rv-ip_wf,
req_witness,
rv-0_wf,
inner-product-space_subtype,
rv-add-0
Rules used in proof :
addEquality,
minusEquality,
productElimination,
dependent_functionElimination,
isect_memberEquality,
independent_isectElimination,
instantiate,
independent_functionElimination,
natural_numberEquality,
because_Cache,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x:Point]. (x \mcdot{} 0 = r0)
Date html generated:
2016_11_08-AM-09_15_05
Last ObjectModification:
2016_10_31-PM-03_03_53
Theory : inner!product!spaces
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