Nuprl Lemma : inner-product-space_wf
InnerProductSpace ∈ 𝕌'
Proof
Definitions occuring in Statement :
inner-product-space: InnerProductSpace,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
implies: P ⇒ Q,
all: ∀x:A. B[x],
guard: {T},
btrue: tt,
ifthenelse: if b then t else f fi ,
eq_atom: x =a y,
record-select: r.x,
record+: record+,
prop: ℙ,
so_apply: x[s],
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
inner-product-space: InnerProductSpace
Lemmas referenced :
int-to-real_wf,
rless_wf,
rv-0_wf,
ss-sep_wf,
subtype_rel_self,
rmul_wf,
rv-mul_wf,
radd_wf,
rv-add_wf,
req_wf,
all_wf,
real_wf,
real-vector-space_subtype1,
ss-point_wf,
record+_wf,
real-vector-space_wf
Rules used in proof :
rename,
setElimination,
natural_numberEquality,
dependentIntersectionElimination,
tokenEquality,
functionExtensionality,
productEquality,
because_Cache,
universeEquality,
cumulativity,
applyEquality,
hypothesisEquality,
functionEquality,
setEquality,
lambdaEquality,
sqequalRule,
equalitySymmetry,
equalityTransitivity,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
introduction,
cut,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
InnerProductSpace \mmember{} \mBbbU{}'
Date html generated:
2016_11_08-AM-09_14_34
Last ObjectModification:
2016_10_31-PM-02_28_11
Theory : inner!product!spaces
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