### Nuprl Lemma : seq-max-lower_wf

`∀[k,n:ℕ]. ∀[f:ℕ+ ⟶ ℤ].  (seq-max-lower(k;n;f) ∈ ℕ+)`

Proof

Definitions occuring in Statement :  seq-max-lower: `seq-max-lower(k;n;f)` nat_plus: `ℕ+` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` int: `ℤ`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` seq-max-lower: `seq-max-lower(k;n;f)` nat_plus: `ℕ+` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` true: `True` and: `P ∧ Q` prop: `ℙ` int_seg: `{i..j-}` nat: `ℕ` le: `A ≤ B` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` iff: `P `⇐⇒` Q` not: `¬A` rev_implies: `P `` Q` implies: `P `` Q` false: `False` uiff: `uiff(P;Q)` uimplies: `b supposing a` lelt: `i ≤ j < k` subtract: `n - m` subtype_rel: `A ⊆r B` top: `Top` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` bfalse: `ff`
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation imageMemberEquality baseClosed lambdaEquality multiplyEquality addEquality setElimination rename because_Cache applyEquality functionExtensionality productElimination dependent_functionElimination unionElimination lambdaFormation voidElimination independent_functionElimination independent_isectElimination isect_memberEquality voidEquality intEquality minusEquality equalityElimination equalityTransitivity equalitySymmetry axiomEquality functionEquality

Latex:
\mforall{}[k,n:\mBbbN{}].  \mforall{}[f:\mBbbN{}\msupplus{}  {}\mrightarrow{}  \mBbbZ{}].    (seq-max-lower(k;n;f)  \mmember{}  \mBbbN{}\msupplus{})

Date html generated: 2017_10_03-AM-08_43_58
Last ObjectModification: 2017_09_12-PM-00_25_50

Theory : reals

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