Nuprl Lemma : swap_wf
∀[T:Type]. ∀[L:T List]. ∀[i,j:ℕ||L||]. (swap(L;i;j) ∈ T List)
Proof
Definitions occuring in Statement :
swap: swap(L;i;j),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
swap: swap(L;i;j)
Lemmas referenced :
permute_list_wf,
flip_wf,
length_wf_nat,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality,
natural_numberEquality,
universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[i,j:\mBbbN{}||L||]. (swap(L;i;j) \mmember{} T List)
Date html generated:
2019_10_15-AM-10_57_57
Last ObjectModification:
2018_09_27-AM-09_37_29
Theory : list!
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