Nuprl Lemma : length_firstn_eq
∀[A:Type]. ∀[as:A List]. ∀[n:{0...||as||}]. (||firstn(n;as)|| = n ∈ ℤ)
Proof
Definitions occuring in Statement :
firstn: firstn(n;as),
length: ||as||,
list: T List,
int_iseg: {i...j},
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_iseg: {i...j}
Lemmas referenced :
length_firstn,
int_iseg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
natural_numberEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as:A List]. \mforall{}[n:\{0...||as||\}]. (||firstn(n;as)|| = n)
Date html generated:
2016_05_14-AM-06_48_23
Last ObjectModification:
2015_12_26-PM-00_24_23
Theory : list_0
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