Nuprl Lemma : satisfies-integer-inequality_wf
∀[xs,as:ℤ List]. (xs ⋅ as ≥0 ∈ ℙ)
Proof
Definitions occuring in Statement :
satisfies-integer-inequality: xs ⋅ as ≥0,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
satisfies-integer-inequality: xs ⋅ as ≥0,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
ge: i ≥ j
Lemmas referenced :
list_wf,
integer-dot-product_wf,
ge_wf,
less_than_wf,
int_subtype_base,
list_subtype_base,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
independent_isectElimination,
hypothesis,
because_Cache,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[xs,as:\mBbbZ{} List]. (xs \mcdot{} as \mgeq{}0 \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_56_17
Last ObjectModification:
2016_01_14-PM-08_44_37
Theory : omega
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