Nuprl Lemma : swap_length
∀[T:Type]. ∀[L:T List]. ∀[i,j:ℕ||L||]. (||swap(L;i;j)|| = ||L|| ∈ ℤ)
Proof
Definitions occuring in Statement :
swap: swap(L;i;j),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
swap: swap(L;i;j),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
permute_list_length,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
natural_numberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[i,j:\mBbbN{}||L||]. (||swap(L;i;j)|| = ||L||)
Date html generated:
2016_05_15-PM-02_04_13
Last ObjectModification:
2015_12_27-AM-00_22_12
Theory : list!
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