Nuprl Lemma : qlf-val_wf
∀[n:ℕ]. ∀[lf:q-linear-form(n)]. ∀[p:ℚ^n]. (qlf-val(lf;p) ∈ ℚ)
Proof
Definitions occuring in Statement :
qlf-val: qlf-val(lf;p),
q-linear-form: q-linear-form(n),
qvn: ℚ^n,
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qlf-val: qlf-val(lf;p),
q-linear-form: q-linear-form(n),
qvn: ℚ^n,
uimplies: b supposing a
Lemmas referenced :
qadd_wf,
qdot_wf,
qvn_wf,
q-linear-form_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
lemma_by_obid,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[lf:q-linear-form(n)]. \mforall{}[p:\mBbbQ{}\^{}n]. (qlf-val(lf;p) \mmember{} \mBbbQ{})
Date html generated:
2016_05_15-PM-11_22_39
Last ObjectModification:
2015_12_27-PM-07_31_51
Theory : rationals
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