Nuprl Lemma : seq-cons-item
∀[T:Type]. ∀[a:Top]. ∀[s:sequence(T)]. ∀[i:Top]. (seq-cons(a;s)[i] ~ if (i =z 0) then a else s[i - 1] fi )
Proof
Definitions occuring in Statement :
seq-cons: seq-cons(a;s),
seq-item: s[i],
sequence: sequence(T),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
top: Top,
subtract: n - m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sequence: sequence(T),
seq-item: s[i],
seq-cons: seq-cons(a;s),
pi2: snd(t)
Lemmas referenced :
top_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
isect_memberEquality,
isectElimination,
hypothesisEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:Top]. \mforall{}[s:sequence(T)]. \mforall{}[i:Top].
(seq-cons(a;s)[i] \msim{} if (i =\msubz{} 0) then a else s[i - 1] fi )
Date html generated:
2018_07_25-PM-01_29_01
Last ObjectModification:
2018_06_12-PM-10_29_47
Theory : arithmetic
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