Nuprl Lemma : rv-add-sep-iff
∀rv:InnerProductSpace. ∀a,b,h:Point. (h + a # h + b ⇐⇒ a # b)
Proof
Definitions occuring in Statement :
inner-product-space: InnerProductSpace,
rv-add: x + y,
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
implies: P ⇒ Q,
rv-sub: x - y,
rv-minus: -x,
rev_uimplies: rev_uimplies(P;Q),
req_int_terms: t1 ≡ t2,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ
Lemmas referenced :
ss-point_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
ss-eq_wf,
rv-sub_wf,
rv-add_wf,
rv-mul_wf,
int-to-real_wf,
radd_wf,
itermSubtract_wf,
itermAdd_wf,
itermConstant_wf,
req-iff-rsub-is-0,
rv-0_wf,
uiff_transitivity,
ss-eq_functionality,
rv-add_functionality,
ss-eq_weakening,
rv-mul-linear,
rv-add-assoc,
ss-eq_transitivity,
rv-add-swap,
rv-add-comm,
rv-mul-1-add-alt,
rv-mul_functionality,
rv-mul0,
rv-0-add,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_const_lemma,
rv-sep-iff,
ss-sep_wf,
iff_wf,
ss-sep_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
instantiate,
independent_isectElimination,
sqequalRule,
because_Cache,
minusEquality,
natural_numberEquality,
productElimination,
independent_functionElimination,
dependent_functionElimination,
approximateComputation,
lambdaEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
addLevel,
independent_pairFormation,
impliesFunctionality
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}a,b,h:Point. (h + a \# h + b \mLeftarrow{}{}\mRightarrow{} a \# b)
Date html generated:
2017_10_04-PM-11_51_59
Last ObjectModification:
2017_06_26-PM-06_18_05
Theory : inner!product!spaces
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