### Nuprl Lemma : stamps-example

`∀n:ℕ. ∃i:ℕ. (∃j:ℕ [((n + 8) = ((3 * i) + (5 * j)) ∈ ℤ)])`

Proof

Definitions occuring in Statement :  nat: `ℕ` all: `∀x:A. B[x]` sq_exists: `∃x:A [B[x]]` exists: `∃x:A. B[x]` multiply: `n * m` add: `n + m` natural_number: `\$n` int: `ℤ` equal: `s = t ∈ T`
Definitions unfolded in proof :  all: `∀x:A. B[x]` implies: `P `` Q` exists: `∃x:A. B[x]` member: `t ∈ T` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` subtype_rel: `A ⊆r B` nat: `ℕ` so_apply: `x[s]` uimplies: `b supposing a` sq_exists: `∃x:A [B[x]]` prop: `ℙ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` top: `Top` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` guard: `{T}` subtract: `n - m` true: `True` sq_stable: `SqStable(P)` squash: `↓T` sq_type: `SQType(T)` nat_plus: `ℕ+` less_than: `a < b` adjust_div: `adjust_div(b;a)`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :lambdaFormation_alt,  cut thin rename setElimination sqequalRule Error :productIsType,  Error :universeIsType,  introduction extract_by_obid hypothesis sqequalHypSubstitution isectElimination Error :lambdaEquality_alt,  intEquality baseApply closedConclusion baseClosed hypothesisEquality applyEquality natural_numberEquality Error :inhabitedIsType,  independent_isectElimination Error :setIsType,  because_Cache Error :dependent_set_memberEquality_alt,  independent_pairFormation Error :isect_memberEquality_alt,  voidElimination Error :equalityIsType4,  Error :dependent_pairFormation_alt,  Error :dependent_set_memberFormation_alt,  productElimination equalityTransitivity equalitySymmetry dependent_functionElimination unionElimination cutEval Error :equalityIsType1,  addEquality independent_functionElimination minusEquality imageMemberEquality imageElimination multiplyEquality promote_hyp instantiate cumulativity hyp_replacement

Latex:
\mforall{}n:\mBbbN{}.  \mexists{}i:\mBbbN{}.  (\mexists{}j:\mBbbN{}  [((n  +  8)  =  ((3  *  i)  +  (5  *  j)))])

Date html generated: 2019_06_20-PM-00_26_09
Last ObjectModification: 2018_10_09-AM-09_30_44

Theory : int_1

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