Nuprl Lemma : qv-constrained-sup_wf
∀[n:ℕ]. ∀[S,lfs:q-linear-form(n) List]. ∀[p:ℚ^n]. ∀[r:ℚ]. qv-constrained-sup(n;S;lfs;p;r) ∈ ℙ supposing 0 < ||lfs||
Proof
Definitions occuring in Statement :
qv-constrained-sup: qv-constrained-sup(n;S;lfs;p;r),
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],
prop: ℙ,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
qv-constrained-sup: qv-constrained-sup(n;S;lfs;p;r),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
and_wf,
qv-constrained_wf,
equal_wf,
rationals_wf,
qlfs-min-val_wf,
all_wf,
qvn_wf,
qle_wf,
less_than_wf,
length_wf,
q-linear-form_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,
independent_isectElimination,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[S,lfs:q-linear-form(n) List]. \mforall{}[p:\mBbbQ{}\^{}n]. \mforall{}[r:\mBbbQ{}].
qv-constrained-sup(n;S;lfs;p;r) \mmember{} \mBbbP{} supposing 0 < ||lfs||
Date html generated:
2016_05_15-PM-11_23_29
Last ObjectModification:
2015_12_27-PM-07_31_16
Theory : rationals
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