Nuprl Lemma : seq-len-truncate
∀[T:Type]. ∀[s:sequence(T)]. ∀[n:Top]. (||seq-truncate(s;n)|| ~ n)
Proof
Definitions occuring in Statement :
seq-truncate: seq-truncate(s;n),
seq-len: ||s||,
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-truncate: seq-truncate(s;n),
seq-len: ||s||,
pi1: fst(t)
Lemmas referenced :
top_wf,
sequence_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
sqequalAxiom,
cut,
extract_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[n:Top]. (||seq-truncate(s;n)|| \msim{} n)
Date html generated:
2018_07_25-PM-01_28_43
Last ObjectModification:
2018_06_11-PM-11_36_19
Theory : arithmetic
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