Nuprl Lemma : isOdd-add
∀[n,m:ℤ]. uiff(↑isOdd(n + m);¬↑same-parity(n;m))
Proof
Definitions occuring in Statement :
same-parity: same-parity(n;m),
isOdd: isOdd(n),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
not: ¬A,
add: n + m,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
isOdd-isEven-add,
assert_witness,
assert_wf,
same-parity_wf,
isOdd_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
hypothesis,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
lambdaEquality,
dependent_functionElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
intEquality,
voidElimination,
addEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. uiff(\muparrow{}isOdd(n + m);\mneg{}\muparrow{}same-parity(n;m))
Date html generated:
2016_05_14-PM-04_24_42
Last ObjectModification:
2015_12_26-PM-08_20_03
Theory : num_thy_1
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