### Nuprl Lemma : ni-max_wf

`∀[f,g:ℕ∞].  (ni-max(f;g) ∈ ℕ∞)`

Proof

Definitions occuring in Statement :  ni-max: `ni-max(f;g)` nat-inf: `ℕ∞` uall: `∀[x:A]. B[x]` member: `t ∈ T`
Definitions unfolded in proof :  nat-inf: `ℕ∞` uall: `∀[x:A]. B[x]` member: `t ∈ T` ni-max: `ni-max(f;g)` all: `∀x:A. B[x]` implies: `P `` Q` uiff: `uiff(P;Q)` and: `P ∧ Q` rev_uimplies: `rev_uimplies(P;Q)` uimplies: `b supposing a` prop: `ℙ` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` so_lambda: `λ2x.t[x]` so_apply: `x[s]` guard: `{T}`
Lemmas referenced :  bool_wf set_wf all_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 assert_wf assert_of_bor nat_wf bor_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut setElimination thin rename sqequalRule dependent_set_memberEquality lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination applyEquality hypothesisEquality hypothesis lambdaFormation dependent_functionElimination productElimination independent_isectElimination because_Cache addEquality natural_numberEquality unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll functionEquality axiomEquality equalityTransitivity equalitySymmetry inlFormation inrFormation independent_functionElimination

Latex:
\mforall{}[f,g:\mBbbN{}\minfty{}].    (ni-max(f;g)  \mmember{}  \mBbbN{}\minfty{})

Date html generated: 2016_05_15-PM-01_48_04
Last ObjectModification: 2016_01_15-PM-11_16_13

Theory : basic

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