### Nuprl Lemma : ni-max-zero

`∀[x:ℕ∞]. (ni-max(x;0∞) = x ∈ ℕ∞)`

Proof

Definitions occuring in Statement :  ni-max: `ni-max(f;g)` nat2inf: `n∞` nat-inf: `ℕ∞` uall: `∀[x:A]. B[x]` natural_number: `\$n` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` nat-inf: `ℕ∞` squash: `↓T` so_lambda: `λ2x.t[x]` ge: `i ≥ j ` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` so_apply: `x[s]` nat2inf: `n∞` ni-max: `ni-max(f;g)` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` uiff: `uiff(P;Q)` bor: `p ∨bq` ifthenelse: `if b then t else f fi ` bfalse: `ff` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  ni-max_wf nat2inf_wf false_wf le_wf all_wf nat_wf assert_wf nat_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_wf itermAdd_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_add_lemma int_term_value_var_lemma int_formula_prop_wf nat-inf_wf bool_wf eqtt_to_assert btrue_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot iff_imp_equal_bool lt_int_wf bfalse_wf intformless_wf int_formula_prop_less_lemma less_than_wf assert_of_lt_int iff_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut introduction extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis applyLambdaEquality setElimination rename imageMemberEquality baseClosed imageElimination lambdaEquality functionEquality applyEquality functionExtensionality addEquality dependent_functionElimination because_Cache unionElimination independent_isectElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll equalityElimination equalityTransitivity equalitySymmetry productElimination promote_hyp instantiate cumulativity independent_functionElimination addLevel impliesFunctionality

Latex:
\mforall{}[x:\mBbbN{}\minfty{}].  (ni-max(x;0\minfty{})  =  x)

Date html generated: 2017_10_01-AM-08_29_56
Last ObjectModification: 2017_07_26-PM-04_24_14

Theory : basic

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