Nuprl Lemma : is_prime_wf
∀[n:ℕ]. (is_prime(n) ∈ 𝔹)
Proof
Definitions occuring in Statement :
is_prime: is_prime(n),
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is_prime: is_prime(n),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
nat: ℕ,
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
isl: isl(x)
Lemmas referenced :
decidable__prime,
subtype_rel_self,
nat_wf,
decidable_wf,
prime_wf,
btrue_wf,
bfalse_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
functionEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (is\_prime(n) \mmember{} \mBbbB{})
Date html generated:
2018_05_21-PM-06_59_03
Last ObjectModification:
2018_05_19-PM-04_41_40
Theory : general
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