Nuprl Lemma : decidable__prime
∀n:ℕ. Dec(prime(n))
Proof
Definitions occuring in Statement :
prime: prime(a),
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
nat: ℕ,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
atomic: atomic(a),
cand: A c∧ B
Lemmas referenced :
nat_wf,
prime_imp_atomic,
prime_wf,
atomic_imp_prime,
atomic_wf,
decidable_functionality,
not_wf,
equal_wf,
assoced_wf,
decidable__and2,
and_wf,
reducible_wf,
decidable__not,
decidable__equal_int,
decidable__assoced,
decidable__reducible
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
hypothesis,
independent_pairFormation,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productElimination,
intEquality,
natural_numberEquality,
because_Cache,
isect_memberEquality
Latex:
\mforall{}n:\mBbbN{}. Dec(prime(n))
Date html generated:
2016_05_14-PM-04_21_23
Last ObjectModification:
2015_12_26-PM-08_17_30
Theory : num_thy_1
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