Nuprl Lemma : fact_unroll
∀[n:ℤ]. ((n)! ~ if (n =z 0) then 1 else n * (n - 1)! fi )
Proof
Definitions occuring in Statement :
fact: (n)!,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
multiply: n * m,
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fact: (n)!,
top: Top
Lemmas referenced :
primrec-unroll,
subtract-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
natural_numberEquality,
sqequalAxiom,
intEquality
Latex:
\mforall{}[n:\mBbbZ{}]. ((n)! \msim{} if (n =\msubz{} 0) then 1 else n * (n - 1)! fi )
Date html generated:
2016_05_15-PM-04_04_53
Last ObjectModification:
2015_12_27-PM-03_03_53
Theory : general
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