Nuprl Lemma : qlfs-min-val_wf
∀[n:ℕ]. ∀[lfs:q-linear-form(n) List]. ∀[p:ℚ^n]. qlfs-min-val(lfs;p) ∈ ℚ supposing 0 < ||lfs||
Proof
Definitions occuring in Statement :
qlfs-min-val: qlfs-min-val(lfs;p),
q-linear-form: q-linear-form(n),
qvn: ℚ^n,
rationals: ℚ,
length: ||as||,
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
qlfs-min-val: qlfs-min-val(lfs;p),
top: Top,
prop: ℙ
Lemmas referenced :
qmin-list_wf,
map_wf,
q-linear-form_wf,
rationals_wf,
qlf-val_wf,
map-length,
less_than_wf,
length_wf,
qvn_wf,
list_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[lfs:q-linear-form(n) List]. \mforall{}[p:\mBbbQ{}\^{}n]. qlfs-min-val(lfs;p) \mmember{} \mBbbQ{} supposing 0 < ||lfs||
Date html generated:
2016_05_15-PM-11_22_49
Last ObjectModification:
2015_12_27-PM-07_32_26
Theory : rationals
Home
Index