Nuprl Lemma : separable-translation-group_wf
∀[rv:InnerProductSpace]. ∀[e:Point]. ∀[T:ℝ ⟶ Point ⟶ Point]. (separable-translation-group(rv;e;T) ∈ ℙ)
Proof
Definitions occuring in Statement :
separable-translation-group: separable-translation-group(rv;e;T),
inner-product-space: InnerProductSpace,
real: ℝ,
ss-point: Point,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
separable-translation-group: separable-translation-group(rv;e;T),
prop: ℙ,
and: P ∧ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a
Lemmas referenced :
translation-group-fun_wf,
real_wf,
separable-kernel_wf,
req_wf,
rv-ip_wf,
int-to-real_wf,
ss-point_wf,
trans-kernel_wf,
real-vector-space_subtype1,
inner-product-space_subtype,
subtype_rel_transitivity,
inner-product-space_wf,
real-vector-space_wf,
separation-space_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
functionExtensionality,
applyEquality,
hypothesis,
isectElimination,
because_Cache,
lambdaEquality,
lambdaFormation,
natural_numberEquality,
setElimination,
rename,
dependent_set_memberEquality,
setEquality,
instantiate,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality
Latex:
\mforall{}[rv:InnerProductSpace]. \mforall{}[e:Point]. \mforall{}[T:\mBbbR{} {}\mrightarrow{} Point {}\mrightarrow{} Point].
(separable-translation-group(rv;e;T) \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-00_26_00
Last ObjectModification:
2017_07_01-PM-10_23_42
Theory : inner!product!spaces
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