Nuprl Lemma : prime_wf
∀[a:ℤ]. (prime(a) ∈ ℙ)
Proof
Definitions occuring in Statement :
prime: prime(a),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prime: prime(a),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
or: P ∨ Q,
all: ∀x:A. B[x]
Lemmas referenced :
not_wf,
equal-wf-base,
int_subtype_base,
assoced_wf,
all_wf,
divides_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
applyEquality,
hypothesis,
baseClosed,
natural_numberEquality,
lambdaEquality,
functionEquality,
multiplyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType
Latex:
\mforall{}[a:\mBbbZ{}]. (prime(a) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_22_53
Last ObjectModification:
2018_09_26-PM-05_49_11
Theory : num_thy_1
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