Nuprl Lemma : ml-int-vec-mul_wf
∀[a:ℤ]. ∀[as:ℤ List]. (ml-int-vec-mul(a;as) ∈ ℤ List)
Proof
Definitions occuring in Statement :
ml-int-vec-mul: ml-int-vec-mul(a;as),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ml-int-vec-mul: ml-int-vec-mul(a;as),
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B
Lemmas referenced :
ml-map_wf,
int-valueall-type,
int-value-type,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
independent_isectElimination,
hypothesis,
independent_pairFormation,
productElimination,
lambdaEquality,
multiplyEquality,
hypothesisEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[as:\mBbbZ{} List]. (ml-int-vec-mul(a;as) \mmember{} \mBbbZ{} List)
Date html generated:
2017_09_29-PM-05_56_41
Last ObjectModification:
2017_05_19-PM-05_43_52
Theory : omega
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