Nuprl Lemma : rv-add_functionality
∀[rv:RealVectorSpace]. ∀[x,y,x',y':Point].  (x + y ≡ x' + y') supposing (y ≡ y' and x ≡ x')
Proof
Definitions occuring in Statement : 
rv-add: x + y
, 
real-vector-space: RealVectorSpace
, 
ss-eq: x ≡ y
, 
ss-point: Point
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
false: False
, 
prop: ℙ
, 
or: P ∨ Q
, 
subtype_rel: A ⊆r B
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
ss-eq: x ≡ y
, 
uimplies: b supposing a
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
ss-sep-symmetry, 
real-vector-space_wf, 
ss-point_wf, 
ss-eq_wf, 
ss-sep_wf, 
rv-add-sep2, 
rv-add-sep1, 
rv-add_wf, 
real-vector-space_subtype1, 
ss-sep-or
Rules used in proof : 
voidElimination, 
equalitySymmetry, 
equalityTransitivity, 
isect_memberEquality, 
lambdaEquality, 
because_Cache, 
unionElimination, 
independent_functionElimination, 
isectElimination, 
sqequalRule, 
hypothesis, 
applyEquality, 
hypothesisEquality, 
thin, 
dependent_functionElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
lambdaFormation, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace].  \mforall{}[x,y,x',y':Point].    (x  +  y  \mequiv{}  x'  +  y')  supposing  (y  \mequiv{}  y'  and  x  \mequiv{}  x')
Date html generated:
2016_11_08-AM-09_13_26
Last ObjectModification:
2016_10_31-PM-06_21_36
Theory : inner!product!spaces
Home
Index