Nuprl Lemma : seq-add-item
∀[T:Type]. ∀[s:sequence(T)]. ∀[x,i:Top]. (seq-add(s;x)[i] ~ if i <z ||s|| then s[i] else x fi )
Proof
Definitions occuring in Statement :
seq-add: seq-add(s;x),
seq-item: s[i],
seq-len: ||s||,
sequence: sequence(T),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
pi2: snd(t),
pi1: fst(t),
seq-add: seq-add(s;x),
seq-len: ||s||,
seq-item: s[i],
sequence: sequence(T),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
sequence_wf,
top_wf
Rules used in proof :
universeEquality,
hypothesisEquality,
isectElimination,
hypothesis,
extract_by_obid,
cut,
because_Cache,
sqequalAxiom,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[x,i:Top]. (seq-add(s;x)[i] \msim{} if i <z ||s|| then s[i] else x fi )
Date html generated:
2018_07_25-PM-01_29_47
Last ObjectModification:
2018_06_19-AM-10_16_27
Theory : arithmetic
Home
Index