Nuprl Lemma : rv-sub-add
∀[rv:InnerProductSpace]. ∀[x,v:Point]. x - v + v ≡ x
Proof
Definitions occuring in Statement :
rv-sub: x - y,
inner-product-space: InnerProductSpace,
rv-add: x + y,
ss-eq: x ≡ y,
ss-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rv-sub: x - y,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
ss-sep_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
rv-add_wf,
rv-sub_wf,
ss-point_wf,
ss-eq_wf,
rv-minus_wf,
rv-0_wf,
ss-eq_weakening,
uiff_transitivity,
ss-eq_functionality,
ss-eq_transitivity,
ss-eq_inversion,
rv-add-assoc,
rv-add_functionality,
rv-add-minus,
rv-0-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
isect_memberEquality,
voidElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[x,v:Point]. x - v + v \mequiv{} x
Date html generated:
2017_10_04-PM-11_51_25
Last ObjectModification:
2017_06_21-AM-11_53_09
Theory : inner!product!spaces
Home
Index