Nuprl Lemma : rv-sep-or
∀rv:InnerProductSpace. ∀a:Point. ∀b:{b:Point| a # b} . ∀c:Point. (a # c ∨ b # c)
Proof
Definitions occuring in Statement :
inner-product-space: InnerProductSpace,
ss-sep: x # y,
ss-point: Point,
all: ∀x:A. B[x],
or: P ∨ Q,
set: {x:A| B[x]}
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
ss-sep-or,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf,
sq_stable__rv-sep-ext,
ss-point_wf,
set_wf,
ss-sep_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
instantiate,
isectElimination,
independent_isectElimination,
sqequalRule,
setElimination,
rename,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality,
because_Cache
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}a:Point. \mforall{}b:\{b:Point| a \# b\} . \mforall{}c:Point. (a \# c \mvee{} b \# c)
Date html generated:
2017_10_04-PM-11_51_48
Last ObjectModification:
2017_03_15-PM-09_03_52
Theory : inner!product!spaces
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