Nuprl Lemma : odd-iff-not-even
∀[n:ℤ]. uiff(↑isOdd(n);¬↑isEven(n))
Proof
Definitions occuring in Statement :
isEven: isEven(n),
isOdd: isOdd(n),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
guard: {T},
prop: ℙ,
or: P ∨ Q
Lemmas referenced :
odd-implies,
assert_wf,
isEven_wf,
isOdd_wf,
odd-or-even,
assert_of_bor,
assert_witness,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaFormation,
thin,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
productElimination,
voidElimination,
isectElimination,
sqequalRule,
lambdaEquality,
because_Cache,
independent_isectElimination,
unionElimination,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality
Latex:
\mforall{}[n:\mBbbZ{}]. uiff(\muparrow{}isOdd(n);\mneg{}\muparrow{}isEven(n))
Date html generated:
2016_05_14-PM-04_24_06
Last ObjectModification:
2015_12_26-PM-08_19_28
Theory : num_thy_1
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