Nuprl Lemma : rv-sep-witness_wf
∀rv:InnerProductSpace. ∀x:Point. ∀y:{y:Point| x # y} . (rv-sep-witness(rv;x;y) ∈ x # y)
Proof
Definitions occuring in Statement :
rv-sep-witness: rv-sep-witness(rv;x;y),
inner-product-space: InnerProductSpace,
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
rv-sep-witness: rv-sep-witness(rv;x;y),
record-select: r.x,
sq_stable__rv-sep-ext,
squash: ↓T,
so_apply: x[s],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
sq_stable_wf,
all_wf,
sq_stable__rv-sep-ext,
ss-sep_wf,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
inner-product-space_subtype,
real-vector-space_subtype1,
ss-point_wf,
set_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
baseClosed,
imageMemberEquality,
universeEquality,
cumulativity,
because_Cache,
lambdaEquality,
sqequalRule,
independent_isectElimination,
instantiate,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
introduction,
hypothesis,
sqequalHypSubstitution,
rename,
thin,
setElimination,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}x:Point. \mforall{}y:\{y:Point| x \# y\} . (rv-sep-witness(rv;x;y) \mmember{} x \# y)
Date html generated:
2016_11_08-AM-09_16_42
Last ObjectModification:
2016_11_03-AM-10_58_46
Theory : inner!product!spaces
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