### Nuprl Lemma : div-positive-1

`∀n:ℕ+. ∀i:{1..n + 1-}.  0 < n ÷ i`

Proof

Definitions occuring in Statement :  int_seg: `{i..j-}` nat_plus: `ℕ+` less_than: `a < b` all: `∀x:A. B[x]` divide: `n ÷ m` add: `n + m` natural_number: `\$n`
Definitions unfolded in proof :  all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` member: `t ∈ T` subtype_rel: `A ⊆r B` nat_plus: `ℕ+` uimplies: `b supposing a` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` top: `Top` true: `True` subtract: `n - m` int_seg: `{i..j-}` int_nzero: `ℤ-o` so_lambda: `λ2x.t[x]` lelt: `i ≤ j < k` so_apply: `x[s]` nequal: `a ≠ b ∈ T ` rev_uimplies: `rev_uimplies(P;Q)` guard: `{T}` sq_type: `SQType(T)` sq_stable: `SqStable(P)` squash: `↓T`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality applyEquality hypothesis sqequalRule natural_numberEquality addEquality setElimination rename independent_isectElimination independent_pairFormation dependent_functionElimination productElimination unionElimination voidElimination independent_functionElimination lambdaEquality isect_memberEquality voidEquality intEquality because_Cache minusEquality setEquality inlFormation inrFormation addLevel orFunctionality instantiate cumulativity equalityTransitivity equalitySymmetry multiplyEquality introduction imageMemberEquality baseClosed imageElimination

Latex:
\mforall{}n:\mBbbN{}\msupplus{}.  \mforall{}i:\{1..n  +  1\msupminus{}\}.    0  <  n  \mdiv{}  i

Date html generated: 2016_05_13-PM-03_35_39
Last ObjectModification: 2016_01_14-PM-06_39_48

Theory : arithmetic

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