Nuprl Lemma : seq-truncate-item
∀[T:Type]. ∀[s:sequence(T)]. ∀[n,i:Top]. (seq-truncate(s;n)[i] ~ s[i])
Proof
Definitions occuring in Statement :
seq-truncate: seq-truncate(s;n),
seq-item: s[i],
sequence: sequence(T),
uall: ∀[x:A]. B[x],
top: Top,
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-truncate: seq-truncate(s;n),
pi2: snd(t)
Lemmas referenced :
top_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
because_Cache,
cut,
extract_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[n,i:Top]. (seq-truncate(s;n)[i] \msim{} s[i])
Date html generated:
2018_07_25-PM-01_28_40
Last ObjectModification:
2018_06_11-PM-11_34_18
Theory : arithmetic
Home
Index