Nuprl Lemma : atomic_imp_prime
∀a:ℤ. prime(a) supposing atomic(a)
Proof
Definitions occuring in Statement :
prime: prime(a),
atomic: atomic(a),
uimplies: b supposing a,
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
atomic: atomic(a),
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
guard: {T},
prime: prime(a),
or: P ∨ Q,
rev_implies: P ⇐ Q,
gcd_p: GCD(a;b;y),
coprime: CoPrime(a,b),
cand: A c∧ B,
assoced: a ~ b
Lemmas referenced :
int_subtype_base,
assoced_wf,
reducible_wf,
atomic_char,
atomic_wf,
istype-int,
divides_wf,
gcd_wf,
gcd_is_divisor_1,
coprime_prod,
coprime_elim_a,
divides_reflexivity,
gcd_is_divisor_2,
divides_functionality_wrt_assoced,
assoced_inversion,
assoced_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
Error :isect_memberFormation_alt,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairEquality,
Error :lambdaEquality_alt,
dependent_functionElimination,
hypothesisEquality,
voidElimination,
Error :equalityIsType4,
Error :inhabitedIsType,
applyEquality,
extract_by_obid,
hypothesis,
natural_numberEquality,
Error :universeIsType,
isectElimination,
rename,
independent_functionElimination,
independent_pairFormation,
multiplyEquality,
because_Cache,
unionElimination,
Error :inlFormation_alt,
independent_isectElimination,
Error :inrFormation_alt
Latex:
\mforall{}a:\mBbbZ{}. prime(a) supposing atomic(a)
Date html generated:
2019_06_20-PM-02_23_56
Last ObjectModification:
2018_10_03-AM-00_12_48
Theory : num_thy_1
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