Nuprl Lemma : qv-constrained-no-inf_wf
∀[n:ℕ]. ∀[S,lfs:q-linear-form(n) List]. qv-constrained-no-inf(n;S;lfs) ∈ ℙ supposing 0 < ||lfs||
Proof
Definitions occuring in Statement :
qv-constrained-no-inf: qv-constrained-no-inf(n;S;lfs),
q-linear-form: q-linear-form(n),
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-no-inf: qv-constrained-no-inf(n;S;lfs),
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x]
Lemmas referenced :
exists_wf,
qvn_wf,
qv-constrained_wf,
all_wf,
qless_wf,
qlfs-max-val_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,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
functionEquality,
independent_isectElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[S,lfs:q-linear-form(n) List]. qv-constrained-no-inf(n;S;lfs) \mmember{} \mBbbP{} supposing 0 < ||lfs||
Date html generated:
2016_05_15-PM-11_23_20
Last ObjectModification:
2015_12_27-PM-07_31_22
Theory : rationals
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