Nuprl Lemma : seq-cons-len
∀[T:Type]. ∀[a:Top]. ∀[s:sequence(T)]. (||seq-cons(a;s)|| ~ ||s|| + 1)
Proof
Definitions occuring in Statement :
seq-cons: seq-cons(a;s),
seq-len: ||s||,
sequence: sequence(T),
uall: ∀[x:A]. B[x],
top: Top,
add: 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-len: ||s||,
seq-cons: seq-cons(a;s),
pi1: fst(t)
Lemmas referenced :
sequence_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
isectElimination,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:Top]. \mforall{}[s:sequence(T)]. (||seq-cons(a;s)|| \msim{} ||s|| + 1)
Date html generated:
2018_07_25-PM-01_29_05
Last ObjectModification:
2018_06_12-PM-10_31_11
Theory : arithmetic
Home
Index