Nuprl Lemma : Prime-isOdd
∀p:Prime. ((¬(p = 2 ∈ ℤ)) 
⇒ (↑isOdd(p)))
Proof
Definitions occuring in Statement : 
Prime: Prime
, 
isOdd: isOdd(n)
, 
assert: ↑b
, 
all: ∀x:A. B[x]
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
squash: ↓T
, 
prop: ℙ
, 
not: ¬A
, 
false: False
, 
less_than': less_than'(a;b)
, 
and: P ∧ Q
, 
le: A ≤ B
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
sq_stable: SqStable(P)
, 
int_upper: {i...}
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
Prime: Prime
, 
implies: P 
⇒ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
Prime_wf, 
equal-wf-T-base, 
not_wf, 
le_wf, 
false_wf, 
int_upper_subtype_nat, 
prime-isOdd, 
isOdd_wf, 
sq_stable__assert
Rules used in proof : 
intEquality, 
imageElimination, 
baseClosed, 
imageMemberEquality, 
independent_pairFormation, 
sqequalRule, 
natural_numberEquality, 
dependent_set_memberEquality, 
applyEquality, 
dependent_functionElimination, 
independent_functionElimination, 
hypothesis, 
hypothesisEquality, 
isectElimination, 
extract_by_obid, 
introduction, 
cut, 
rename, 
thin, 
setElimination, 
sqequalHypSubstitution, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}p:Prime.  ((\mneg{}(p  =  2))  {}\mRightarrow{}  (\muparrow{}isOdd(p)))
Date html generated:
2018_05_21-PM-06_58_02
Last ObjectModification:
2017_12_31-PM-06_12_35
Theory : general
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