Nuprl Lemma : primefactors_wf
∀n:{2...}. (primefactors(n) ∈ {factors:{m:{2...}| prime(m)} List| n = Π(factors) ∈ ℤ} )
Proof
Definitions occuring in Statement :
primefactors: primefactors(n),
mul-list: Π(ns) ,
prime: prime(a),
list: T List,
int_upper: {i...},
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
primefactors: primefactors(n),
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
int_upper: {i...},
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
sq_exists: ∃x:A [B[x]]
Lemmas referenced :
prime-factors3,
all_wf,
int_upper_wf,
sq_exists_wf,
list_wf,
prime_wf,
equal_wf,
mul-list_wf,
subtype_rel_list
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
instantiate,
extract_by_obid,
hypothesis,
introduction,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
sqequalRule,
lambdaEquality,
setEquality,
because_Cache,
setElimination,
rename,
intEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}n:\{2...\}. (primefactors(n) \mmember{} \{factors:\{m:\{2...\}| prime(m)\} List| n = \mPi{}(factors) \} )
Date html generated:
2018_05_21-PM-08_13_30
Last ObjectModification:
2018_05_19-PM-04_55_09
Theory : general
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