### 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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