Nuprl Lemma : rv-minus_functionality
∀[rv:RealVectorSpace]. ∀[x,x':Point]. -x ≡ -x' supposing x ≡ x'
Proof
Definitions occuring in Statement :
rv-minus: -x,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
ss-point: Point,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
prop: ℙ,
subtype_rel: A ⊆r B,
false: False,
implies: P ⇒ Q,
not: ¬A,
ss-eq: x ≡ y,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
rv-minus: -x
Lemmas referenced :
real-vector-space_wf,
ss-point_wf,
ss-eq_wf,
rv-mul_wf,
real-vector-space_subtype1,
ss-sep_wf,
req_weakening,
int-to-real_wf,
rv-mul_functionality
Rules used in proof :
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
applyEquality,
dependent_functionElimination,
lambdaEquality,
independent_isectElimination,
because_Cache,
hypothesis,
natural_numberEquality,
minusEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[x,x':Point]. -x \mequiv{} -x' supposing x \mequiv{} x'
Date html generated:
2016_11_08-AM-09_14_11
Last ObjectModification:
2016_10_31-PM-02_14_47
Theory : inner!product!spaces
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