Nuprl Lemma : shorten-tuple-simplify
∀[p:Top × Top × Top]. (fst(shorten-tuple(p;1)) ~ fst(snd(p)))
Proof
Definitions occuring in Statement :
shorten-tuple: shorten-tuple(x;n),
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
product: x:A × B[x],
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
shorten-tuple: shorten-tuple(x;n),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
btrue: tt,
pi2: snd(t),
subtract: n - m,
bfalse: ff,
pi1: fst(t)
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
hypothesis,
productEquality,
lemma_by_obid
Latex:
\mforall{}[p:Top \mtimes{} Top \mtimes{} Top]. (fst(shorten-tuple(p;1)) \msim{} fst(snd(p)))
Date html generated:
2016_05_14-PM-03_59_06
Last ObjectModification:
2015_12_26-PM-07_21_34
Theory : tuples
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