Nuprl Lemma : rv-add-cancel-right
∀[rv:RealVectorSpace]. ∀[x,y,z:Point]. uiff(y + x ≡ z + x;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 :
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
ss-eq: x ≡ y,
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q)
Lemmas referenced :
rv-add-comm,
ss-eq_functionality,
real-vector-space_wf,
ss-point_wf,
real-vector-space_subtype1,
uiff_wf,
rv-add_wf,
rv-add-cancel-left,
iff_weakening_uiff,
ss-eq_wf,
ss-sep_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
isect_memberEquality,
independent_pairEquality,
cumulativity,
independent_functionElimination,
independent_isectElimination,
productElimination,
addLevel,
because_Cache,
applyEquality,
isectElimination,
extract_by_obid,
voidElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
lambdaEquality,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
introduction,
isect_memberFormation,
independent_pairFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
cut
Latex:
\mforall{}[rv:RealVectorSpace]. \mforall{}[x,y,z:Point]. uiff(y + x \mequiv{} z + x;y \mequiv{} z)
Date html generated:
2016_11_08-AM-09_14_28
Last ObjectModification:
2016_11_01-PM-00_08_51
Theory : inner!product!spaces
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