### Nuprl Lemma : int_lt_to_int_upper_uniform

`∀i:ℤ. ∀[A:{i + 1...} ⟶ ℙ]. ({∀[j:ℤ]. A[j] supposing i < j} `⇐⇒` {∀[j:{i + 1...}]. A[j]})`

Proof

Definitions occuring in Statement :  int_upper: `{i...}` less_than: `a < b` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` so_apply: `x[s]` all: `∀x:A. B[x]` iff: `P `⇐⇒` Q` function: `x:A ⟶ B[x]` add: `n + m` natural_number: `\$n` int: `ℤ`
Definitions unfolded in proof :  guard: `{T}` all: `∀x:A. B[x]` uall: `∀[x:A]. B[x]` iff: `P `⇐⇒` Q` and: `P ∧ Q` implies: `P `` Q` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` so_apply: `x[s]` int_upper: `{i...}` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` rev_implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` le: `A ≤ B` less_than': `less_than'(a;b)` true: `True`
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation isect_memberFormation independent_pairFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin addEquality hypothesisEquality natural_numberEquality hypothesis intEquality lambdaEquality applyEquality dependent_set_memberEquality dependent_functionElimination unionElimination voidElimination productElimination independent_functionElimination independent_isectElimination isect_memberEquality voidEquality because_Cache minusEquality introduction rename functionEquality cumulativity universeEquality setElimination

Latex:
\mforall{}i:\mBbbZ{}.  \mforall{}[A:\{i  +  1...\}  {}\mrightarrow{}  \mBbbP{}].  (\{\mforall{}[j:\mBbbZ{}].  A[j]  supposing  i  <  j\}  \mLeftarrow{}{}\mRightarrow{}  \{\mforall{}[j:\{i  +  1...\}].  A[j]\})

Date html generated: 2016_05_13-PM-04_02_41
Last ObjectModification: 2015_12_26-AM-10_56_41

Theory : int_1

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