Nuprl Lemma : assert-is_prime
∀n:ℕ. (↑is_prime(n) ⇐⇒ prime(n))
Proof
Definitions occuring in Statement :
is_prime: is_prime(n),
prime: prime(a),
nat: ℕ,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
is_prime: is_prime(n),
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
nat: ℕ,
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
true: True,
bfalse: ff,
false: False,
not: ¬A
Lemmas referenced :
nat_wf,
decidable__prime,
subtype_rel_self,
decidable_wf,
prime_wf,
true_wf,
false_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
applyEquality,
thin,
instantiate,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
functionEquality,
setElimination,
rename,
hypothesisEquality,
because_Cache,
unionElimination,
independent_pairFormation,
natural_numberEquality,
voidElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination
Latex:
\mforall{}n:\mBbbN{}. (\muparrow{}is\_prime(n) \mLeftarrow{}{}\mRightarrow{} prime(n))
Date html generated:
2018_05_21-PM-06_59_11
Last ObjectModification:
2018_05_19-PM-04_41_51
Theory : general
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