Nuprl Lemma : increasing-sequence_wf

`∀[a:ℕ ⟶ ℕ]. (increasing-sequence(a) ∈ ℙ)`

Proof

Definitions occuring in Statement :  increasing-sequence: `increasing-sequence(a)` nat: `ℕ` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  so_apply: `x[s]` uiff: `uiff(P;Q)` guard: `{T}` less_than': `less_than'(a;b)` le: `A ≤ B` subtype_rel: `A ⊆r B` prop: `ℙ` and: `P ∧ Q` top: `Top` not: `¬A` implies: `P `` Q` false: `False` exists: `∃x:A. B[x]` satisfiable_int_formula: `satisfiable_int_formula(fmla)` uimplies: `b supposing a` or: `P ∨ Q` decidable: `Dec(P)` all: `∀x:A. B[x]` ge: `i ≥ j ` nat: `ℕ` so_lambda: `λ2x.t[x]` increasing-sequence: `increasing-sequence(a)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  int_formula_prop_eq_lemma intformeq_wf add-is-int-iff false_wf add_nat_wf le_wf int_formula_prop_wf int_term_value_var_lemma int_term_value_add_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermAdd_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties equal_wf or_wf nat_wf all_wf
Rules used in proof :  functionEquality axiomEquality independent_functionElimination productElimination baseClosed closedConclusion baseApply promote_hyp pointwiseFunctionality applyLambdaEquality equalitySymmetry equalityTransitivity lambdaFormation computeAll independent_pairFormation voidEquality voidElimination isect_memberEquality intEquality int_eqEquality dependent_pairFormation independent_isectElimination unionElimination dependent_functionElimination natural_numberEquality rename setElimination addEquality dependent_set_memberEquality hypothesisEquality functionExtensionality applyEquality because_Cache lambdaEquality hypothesis thin isectElimination sqequalHypSubstitution extract_by_obid sqequalRule cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[a:\mBbbN{}  {}\mrightarrow{}  \mBbbN{}].  (increasing-sequence(a)  \mmember{}  \mBbbP{})

Date html generated: 2017_04_20-AM-07_36_30
Last ObjectModification: 2017_04_15-PM-05_03_38

Theory : continuity

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