Nuprl Lemma : iseg-append-nth_tl
∀[T:Type]. ∀[as,bs:T List]. (as @ nth_tl(||as||;bs)) = bs ∈ (T List) supposing as ≤ bs
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
length: ||as||,
nth_tl: nth_tl(n;as),
append: as @ bs,
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
prop: ℙ,
squash: ↓T,
true: True
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
append_wf,
squash_wf,
true_wf,
nth_tl_append,
list_wf,
nth_tl_wf,
length_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
dependent_set_memberEquality,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
because_Cache,
sqequalRule,
natural_numberEquality,
imageMemberEquality,
baseClosed,
hyp_replacement,
Error :applyLambdaEquality,
setElimination,
rename,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (as @ nth\_tl(||as||;bs)) = bs supposing as \mleq{} bs
Date html generated:
2016_10_21-AM-10_35_19
Last ObjectModification:
2016_07_12-AM-05_47_23
Theory : list_1
Home
Index