Nuprl Lemma : append-tuple-shorten-tuple
∀[L:Type List]. ∀[x:tuple-type(L)]. ∀[n:ℕ||L||].
(append-tuple(n;||L|| - n;fst(split-tuple(x;n));shorten-tuple(x;n)) ~ x)
Proof
Definitions occuring in Statement :
append-tuple: append-tuple(n;m;x;y),
shorten-tuple: shorten-tuple(x;n),
split-tuple: split-tuple(x;n),
tuple-type: tuple-type(L),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
pi1: fst(t),
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
top: Top
Lemmas referenced :
append-tuple-split-tuple,
int_seg_wf,
length_wf,
tuple-type_wf,
list_wf,
shorten-tuple-split-tuple,
int_seg_subtype_nat,
false_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
natural_numberEquality,
instantiate,
universeEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[L:Type List]. \mforall{}[x:tuple-type(L)]. \mforall{}[n:\mBbbN{}||L||].
(append-tuple(n;||L|| - n;fst(split-tuple(x;n));shorten-tuple(x;n)) \msim{} x)
Date html generated:
2016_05_14-PM-03_59_02
Last ObjectModification:
2015_12_26-PM-07_21_37
Theory : tuples
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