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
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