Nuprl Lemma : shorten-tuple-append-tuple
∀[L1,L2:Type List].
∀[x:tuple-type(L1)]. ∀[y:tuple-type(L2)].
(shorten-tuple(append-tuple(||L1||;||L2||;x;y);||L1||) = y ∈ tuple-type(L2))
supposing 0 < ||L2||
Proof
Definitions occuring in Statement :
append-tuple: append-tuple(n;m;x;y),
shorten-tuple: shorten-tuple(x;n),
tuple-type: tuple-type(L),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
pi2: snd(t),
prop: ℙ
Lemmas referenced :
shorten-tuple-split-tuple,
length_wf_nat,
split-tuple-append-tuple,
tuple-type_wf,
less_than_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
universeEquality,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
axiomEquality,
because_Cache,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L1,L2:Type List].
\mforall{}[x:tuple-type(L1)]. \mforall{}[y:tuple-type(L2)].
(shorten-tuple(append-tuple(||L1||;||L2||;x;y);||L1||) = y)
supposing 0 < ||L2||
Date html generated:
2016_05_14-PM-03_59_14
Last ObjectModification:
2015_12_26-PM-07_21_42
Theory : tuples
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