Nuprl Lemma : rv-n_wf
∀[n:ℕ]. (vecℝ^n ∈ RealVectorSpace)
Proof
Definitions occuring in Statement :
rv-n: vecℝ^n,
real-vector-space: RealVectorSpace,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-vec: ℝ^n,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
rv-n: vecℝ^n,
rn-ss: sepℝ^n,
ss-point: Error :ss-point,
mk-ss: Error :mk-ss,
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
ss-eq: Error :ss-eq,
ss-sep: Error :ss-sep,
cand: A c∧ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
req-vec: req-vec(n;x;y),
real-vec-add: X + Y,
prop: ℙ,
real-vec-mul: a*X,
subtype_rel: A ⊆r B,
or: P ∨ Q
Lemmas referenced :
int-to-real_wf,
int_seg_wf,
rn-ss_wf,
mk-real-vector-space_wf,
rec_select_update_lemma,
istype-void,
real-vec-add_wf,
not-real-vec-sep-iff-eq,
radd-assoc,
real-vec-sep_wf,
real-vec-add-com,
real-vec-mul_wf,
real_wf,
real-vec-mul-linear,
rmul-identity1,
rmul-zero-both,
rmul_wf,
real-vec-mul-mul,
radd_wf,
rmul-distrib2,
real-vec-sep-add,
subtype_rel_self,
nat_wf,
real-vec_wf,
real-vec-sep-mul,
rneq_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
productElimination,
hypothesis,
universeIsType,
natural_numberEquality,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
dependent_functionElimination,
isect_memberEquality_alt,
voidElimination,
dependent_set_memberEquality_alt,
inhabitedIsType,
lambdaFormation_alt,
independent_isectElimination,
applyEquality,
independent_functionElimination,
because_Cache,
independent_pairFormation,
productIsType,
functionIsType,
instantiate,
functionEquality,
unionEquality,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (vec\mBbbR{}\^{}n \mmember{} RealVectorSpace)
Date html generated:
2020_05_20-PM-01_10_52
Last ObjectModification:
2019_12_10-AM-00_37_31
Theory : inner!product!spaces
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