### Nuprl Lemma : maybe-new_wf

`∀[s:Name]. ∀[avoid:Name List].  (maybe-new(s;avoid) ∈ {s':Name| ¬(s' ∈ avoid)} )`

Proof

Definitions occuring in Statement :  maybe-new: `maybe-new(s;avoid)` name: `Name` l_member: `(x ∈ l)` list: `T List` uall: `∀[x:A]. B[x]` not: `¬A` member: `t ∈ T` set: `{x:A| B[x]} `
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` maybe-new: `maybe-new(s;avoid)` all: `∀x:A. B[x]` implies: `P `` Q` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` iff: `P `⇐⇒` Q` and: `P ∧ Q` prop: `ℙ` rev_implies: `P `` Q` ifthenelse: `if b then t else f fi ` let: let bfalse: `ff` not: `¬A` false: `False` name: `Name` name-deq: `NameDeq` so_lambda: `λ2x.t[x]` so_apply: `x[s]` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` le: `A ≤ B` less_than': `less_than'(a;b)` decidable: `Dec(P)` or: `P ∨ Q` l_member: `(x ∈ l)` cand: `A c∧ B` nat: `ℕ` guard: `{T}` int_seg: `{i..j-}` ge: `i ≥ j ` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` pi1: `fst(t)` uiff: `uiff(P;Q)` inject: `Inj(A;B;f)` squash: `↓T` true: `True`
Lemmas referenced :  deq-member_wf name_wf name-deq_wf bool_wf iff_transitivity equal-wf-T-base assert_wf l_member_wf iff_weakening_uiff eqtt_to_assert assert-deq-member bnot_wf not_wf eqff_to_assert assert_of_bnot equal_wf list_wf list-deq_wf atom-deq_wf append_wf nat-to-str_wf exists_wf nat_wf decidable__exists_int_seg length_wf int_seg_subtype_nat false_wf int_seg_wf decidable__not decidable__l_member decidable__equal_list decidable__atom_equal less_than_wf select_wf nat_properties int_seg_properties decidable__le satisfiable-full-omega-tt intformand_wf intformnot_wf intformle_wf itermConstant_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_var_lemma int_formula_prop_wf all_wf non_neg_length lelt_wf length_wf_nat pigeon-hole add_nat_wf le_wf add-is-int-iff itermAdd_wf intformeq_wf int_term_value_add_lemma int_formula_prop_eq_lemma squash_wf true_wf iff_weakening_equal decidable__equal_int str-to-nat-to-str str-to-nat_wf general-append-cancellation mu-property deq_wf mu_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesis hypothesisEquality lambdaFormation unionElimination equalityElimination equalityTransitivity equalitySymmetry baseClosed independent_functionElimination because_Cache independent_pairFormation dependent_functionElimination productElimination impliesFunctionality voidElimination dependent_set_memberEquality axiomEquality isect_memberEquality atomEquality lambdaEquality addLevel existsFunctionality instantiate natural_numberEquality addEquality applyEquality independent_isectElimination dependent_pairFormation promote_hyp productEquality setElimination rename int_eqEquality intEquality voidEquality computeAll functionExtensionality applyLambdaEquality pointwiseFunctionality baseApply closedConclusion imageElimination universeEquality imageMemberEquality cumulativity inlFormation

Latex:
\mforall{}[s:Name].  \mforall{}[avoid:Name  List].    (maybe-new(s;avoid)  \mmember{}  \{s':Name|  \mneg{}(s'  \mmember{}  avoid)\}  )

Date html generated: 2017_04_17-AM-09_18_29
Last ObjectModification: 2017_02_27-PM-05_22_42

Theory : decidable!equality

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