### Nuprl Lemma : fresh-cname_wf

`∀[I:Cname List]. (fresh-cname(I) ∈ {x:Cname| ¬(x ∈ I)} )`

Proof

Definitions occuring in Statement :  fresh-cname: `fresh-cname(I)` coordinate_name: `Cname` 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` int_upper: `{i...}` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` uimplies: `b supposing a` not: `¬A` implies: `P `` Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` prop: `ℙ` false: `False` subtype_rel: `A ⊆r B` coordinate_name: `Cname` so_lambda: `λ2x.t[x]` so_apply: `x[s]` and: `P ∧ Q` fresh-cname: `fresh-cname(I)` nat_plus: `ℕ+` guard: `{T}` uiff: `uiff(P;Q)` ge: `i ≥ j ` le: `A ≤ B` pi1: `fst(t)` l_member: `(x ∈ l)` l_all: `(∀x∈L.P[x])` cand: `A c∧ B` int_seg: `{i..j-}` nat: `ℕ` squash: `↓T` lelt: `i ≤ j < k` less_than: `a < b` true: `True` iff: `P `⇐⇒` Q` rev_implies: `P `` Q`
Lemmas referenced :  cons_wf int_upper_wf decidable__le full-omega-unsat intformnot_wf intformle_wf itermConstant_wf istype-int int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_formula_prop_wf istype-le subtype_rel_list coordinate_name_wf subtype_rel_sets_simple le_wf intformand_wf itermVar_wf int_formula_prop_and_lemma int_term_value_var_lemma list_wf list-max-property istype-int_upper length_of_cons_lemma add_nat_plus length_wf_nat decidable__lt intformless_wf int_formula_prop_less_lemma istype-less_than nat_plus_properties add-is-int-iff itermAdd_wf intformeq_wf int_term_value_add_lemma int_formula_prop_eq_lemma false_wf list-max_wf non_neg_length length_wf l_member_wf int_upper_properties set_subtype_base equal-wf-base int_subtype_base l_all_wf2 istype-void nat_properties squash_wf true_wf select_cons_tl subtype_rel_self iff_weakening_equal add-subtract-cancel select_cons_tl_sq2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation_alt introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin natural_numberEquality hypothesis dependent_set_memberEquality_alt dependent_functionElimination unionElimination independent_isectElimination approximateComputation independent_functionElimination dependent_pairFormation_alt lambdaEquality_alt Error :memTop,  sqequalRule universeIsType hypothesisEquality voidElimination applyEquality intEquality lambdaFormation_alt int_eqEquality independent_pairFormation axiomEquality equalityTransitivity equalitySymmetry setElimination rename inhabitedIsType applyLambdaEquality pointwiseFunctionality promote_hyp baseApply closedConclusion baseClosed productElimination equalityIstype because_Cache addEquality productIsType sqequalBase setIsType functionIsType imageMemberEquality imageElimination instantiate universeEquality

Latex:
\mforall{}[I:Cname  List].  (fresh-cname(I)  \mmember{}  \{x:Cname|  \mneg{}(x  \mmember{}  I)\}  )

Date html generated: 2020_05_21-AM-10_48_10
Last ObjectModification: 2020_01_01-PM-02_24_19

Theory : cubical!sets

Home Index