Nuprl Lemma : seq-add-len
∀[T:Type]. ∀[s:sequence(T)]. ∀[x:Top]. (||seq-add(s;x)|| ~ ||s|| + 1)
Proof
Definitions occuring in Statement :
seq-add: seq-add(s;x),
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 :
pi1: fst(t),
seq-add: seq-add(s;x),
seq-len: ||s||,
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,
sqequalAxiom,
sqequalRule,
thin,
productElimination,
sqequalHypSubstitution,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[s:sequence(T)]. \mforall{}[x:Top]. (||seq-add(s;x)|| \msim{} ||s|| + 1)
Date html generated:
2018_07_25-PM-01_29_44
Last ObjectModification:
2018_06_19-AM-10_15_07
Theory : arithmetic
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