Nuprl Lemma : ml-int-vec-mul-sq
∀[a:ℤ]. ∀[as:ℤ List]. (ml-int-vec-mul(a;as) ~ a * as)
Proof
Definitions occuring in Statement :
ml-int-vec-mul: ml-int-vec-mul(a;as),
int-vec-mul: a * as,
list: T List,
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
ml-int-vec-mul: ml-int-vec-mul(a;as),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
and: P ∧ Q,
cand: A c∧ B,
int-vec-mul: a * as
Lemmas referenced :
subtype_base_sq,
list_wf,
list_subtype_base,
int_subtype_base,
int-valueall-type,
int-value-type,
int-vec-mul_wf,
ml-map-sq
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
isect_memberEquality,
hypothesisEquality,
because_Cache,
independent_pairFormation,
productElimination,
lambdaEquality,
multiplyEquality
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[as:\mBbbZ{} List]. (ml-int-vec-mul(a;as) \msim{} a * as)
Date html generated:
2017_09_29-PM-05_56_44
Last ObjectModification:
2017_05_19-PM-05_45_04
Theory : omega
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