Nuprl Lemma : rv-add-cancel-left
∀[rv:RealVectorSpace]. ∀[x,y,z:Point]. uiff(x + y ≡ x + z;y ≡ z)
Proof
Definitions occuring in Statement :
rv-add: x + y,
real-vector-space: RealVectorSpace,
ss-eq: x ≡ y,
ss-point: Point,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(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,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
rv-add-0,
rv-add-minus,
rv-add-assoc,
ss-eq_transitivity,
ss-eq_functionality,
uiff_transitivity,
rv-0_wf,
rv-add_functionality,
ss-eq_weakening,
rv-minus_wf,
real-vector-space_wf,
ss-point_wf,
rv-add_wf,
ss-eq_wf,
real-vector-space_subtype1,
ss-sep_wf
Rules used in proof :
independent_isectElimination,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_pairEquality,
productElimination,
voidElimination,
hypothesis,
applyEquality,
isectElimination,
extract_by_obid,
because_Cache,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[x,y,z:Point]. uiff(x + y \mequiv{} x + z;y \mequiv{} z)
Date html generated:
2016_11_08-AM-09_14_24
Last ObjectModification:
2016_11_01-AM-11_53_47
Theory : inner!product!spaces
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