Nuprl Lemma : rv-sub-same
∀[rv:RealVectorSpace]. ∀[x:Point]. x - x ≡ 0
Proof
Definitions occuring in Statement :
rv-sub: x - y,
rv-0: 0,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
ss-point: Point,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ss-eq: x ≡ y,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
rv-sub: x - y,
rv-minus: -x,
all: ∀x:A. B[x],
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top
Lemmas referenced :
ss-sep_wf,
real-vector-space_subtype1,
rv-sub_wf,
rv-0_wf,
ss-point_wf,
real-vector-space_wf,
ss-eq_wf,
rv-mul_wf,
int-to-real_wf,
radd_wf,
rv-add_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
req-iff-rsub-is-0,
uiff_transitivity,
ss-eq_functionality,
rv-mul-1-add,
ss-eq_weakening,
rv-mul_functionality,
rv-mul0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_const_lemma
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,
isect_memberEquality,
voidElimination,
natural_numberEquality,
minusEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
approximateComputation,
intEquality,
voidEquality
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[x:Point]. x - x \mequiv{} 0
Date html generated:
2017_10_04-PM-11_51_15
Last ObjectModification:
2017_07_28-AM-08_53_54
Theory : inner!product!spaces
Home
Index