Nuprl Lemma : rv-permutation-group_wf
∀[rv:InnerProductSpace]. (Perm(rv) ∈ s-Group)
Proof
Definitions occuring in Statement :
rv-permutation-group: Perm(rv),
inner-product-space: InnerProductSpace,
s-group: s-Group,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
prop: ℙ,
all: ∀x:A. B[x],
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
rv-permutation-group: Perm(rv),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
ss-point_wf,
ss-sep_wf,
rv-sep-witness_wf,
separation-space_wf,
real-vector-space_wf,
inner-product-space_wf,
subtype_rel_transitivity,
inner-product-space_subtype,
real-vector-space_subtype1,
permutation-s-group_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
setEquality,
because_Cache,
dependent_set_memberEquality,
rename,
setElimination,
dependent_functionElimination,
lambdaEquality,
independent_isectElimination,
instantiate,
hypothesis,
applyEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[rv:InnerProductSpace]. (Perm(rv) \mmember{} s-Group)
Date html generated:
2016_11_08-AM-09_20_46
Last ObjectModification:
2016_11_03-AM-11_25_51
Theory : inner!product!spaces
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