Nuprl Lemma : rv-sub_functionality
∀[rv:RealVectorSpace]. ∀[x,y,x',y':Point]. (x - y ≡ x' - y') supposing (y ≡ y' and x ≡ x')
Proof
Definitions occuring in Statement :
rv-sub: 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 :
rev_uimplies: rev_uimplies(P;Q),
and: P ∧ Q,
uiff: uiff(P;Q),
all: ∀x:A. B[x],
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-sub: x - y
Lemmas referenced :
rv-minus_functionality,
rv-add_functionality,
ss-eq_functionality,
ss-eq_weakening,
real-vector-space_wf,
ss-point_wf,
ss-eq_wf,
rv-minus_wf,
rv-add_wf,
real-vector-space_subtype1,
ss-sep_wf
Rules used in proof :
productElimination,
independent_isectElimination,
independent_functionElimination,
voidElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
hypothesis,
applyEquality,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
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_15_26
Last ObjectModification:
2016_10_31-PM-11_30_16
Theory : inner!product!spaces
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