### Nuprl Lemma : mod2-2n

`∀n:ℤ. (((2 * n) mod 2) = 0 ∈ ℤ)`

Proof

Definitions occuring in Statement :  modulus: `a mod n` all: `∀x:A. B[x]` multiply: `n * m` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` squash: `↓T` prop: `ℙ` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` implies: `P `` Q` modulus: `a mod n` remainder: `n rem m` decidable: `Dec(P)` or: `P ∨ Q` uiff: `uiff(P;Q)` top: `Top` subtract: `n - m` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` nat_plus: `ℕ+` less_than: `a < b` sq_type: `SQType(T)`
Rules used in proof :  cut sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :lambdaFormation_alt,  introduction extract_by_obid sqequalHypSubstitution isectElimination thin multiplyEquality natural_numberEquality setElimination rename hypothesisEquality hypothesis applyEquality Error :lambdaEquality_alt,  imageElimination equalityTransitivity equalitySymmetry Error :universeIsType,  Error :inhabitedIsType,  instantiate universeEquality intEquality dependent_functionElimination because_Cache sqequalRule imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination unionElimination Error :dependent_set_memberEquality_alt,  minusEquality Error :isect_memberEquality_alt,  voidElimination addEquality independent_pairFormation cumulativity

Latex:
\mforall{}n:\mBbbZ{}.  (((2  *  n)  mod  2)  =  0)

Date html generated: 2019_06_20-AM-11_26_14
Last ObjectModification: 2019_03_15-PM-05_58_07

Theory : arithmetic

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