### Nuprl Lemma : ni-max-nat

`∀[n,m:ℕ].  (ni-max(n∞;m∞) = imax(n;m)∞ ∈ ℕ∞)`

Proof

Definitions occuring in Statement :  ni-max: `ni-max(f;g)` nat2inf: `n∞` nat-inf: `ℕ∞` imax: `imax(a;b)` nat: `ℕ` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat-inf: `ℕ∞` all: `∀x:A. B[x]` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B` nat: `ℕ` ge: `i ≥ j ` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` false: `False` not: `¬A` top: `Top` and: `P ∧ Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` nat2inf: `n∞` ni-max: `ni-max(f;g)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` uiff: `uiff(P;Q)` guard: `{T}`
Lemmas referenced :  int_formula_prop_less_lemma intformless_wf decidable__lt imax_strict_ub assert_of_lt_int assert_of_bor iff_weakening_uiff iff_transitivity iff_wf less_than_wf or_wf imax_wf lt_int_wf bor_wf iff_imp_equal_bool nat_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 nat2inf_wf ni-max_wf assert_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut dependent_set_memberEquality lambdaFormation lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis because_Cache sqequalRule addEquality setElimination rename natural_numberEquality dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll functionEquality axiomEquality functionExtensionality addLevel productElimination impliesFunctionality independent_functionElimination orFunctionality inlFormation inrFormation

Latex:
\mforall{}[n,m:\mBbbN{}].    (ni-max(n\minfty{};m\minfty{})  =  imax(n;m)\minfty{})

Date html generated: 2016_05_15-PM-01_48_08
Last ObjectModification: 2016_01_15-PM-11_16_20

Theory : basic

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