Nuprl Lemma : translation-group-fun_wf
∀rv:InnerProductSpace. ∀e:Point. ∀T:ℝ ⟶ Point ⟶ Point. (translation-group-fun(rv;e;T) ∈ ℙ)
Proof
Definitions occuring in Statement :
translation-group-fun: translation-group-fun(rv;e;T),
inner-product-space: InnerProductSpace,
real: ℝ,
ss-point: Point,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
translation-group-fun: translation-group-fun(rv;e;T),
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
so_apply: x[s],
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
real_wf,
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-sep_wf,
ss-eq_wf,
radd_wf,
exists!_wf,
rv-add_wf,
rv-mul_wf,
rleq_wf,
int-to-real_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
applyEquality,
instantiate,
independent_isectElimination,
because_Cache,
functionEquality,
functionExtensionality,
setEquality,
natural_numberEquality,
setElimination,
rename
Latex:
\mforall{}rv:InnerProductSpace. \mforall{}e:Point. \mforall{}T:\mBbbR{} {}\mrightarrow{} Point {}\mrightarrow{} Point. (translation-group-fun(rv;e;T) \mmember{} \mBbbP{})
Date html generated:
2017_10_05-AM-00_21_07
Last ObjectModification:
2017_06_23-PM-09_42_43
Theory : inner!product!spaces
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