### Nuprl Lemma : bag_remove1_aux_wf

`∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[bs,checked:T List].  (bag_remove1_aux(eq;checked;x;bs) ∈ T List?)`

Proof

Definitions occuring in Statement :  bag_remove1_aux: `bag_remove1_aux(eq;checked;a;as)` list: `T List` deq: `EqDecider(T)` uall: `∀[x:A]. B[x]` unit: `Unit` member: `t ∈ T` union: `left + right` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` nat: `ℕ` implies: `P `` Q` false: `False` ge: `i ≥ j ` uimplies: `b supposing a` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` not: `¬A` top: `Top` and: `P ∧ Q` prop: `ℙ` subtype_rel: `A ⊆r B` guard: `{T}` or: `P ∨ Q` bag_remove1_aux: `bag_remove1_aux(eq;checked;a;as)` so_lambda: `so_lambda(x,y,z.t[x; y; z])` so_apply: `x[s1;s2;s3]` unit: `Unit` cons: `[a / b]` colength: `colength(L)` so_lambda: `λ2x y.t[x; y]` so_apply: `x[s1;s2]` decidable: `Dec(P)` nil: `[]` it: `⋅` so_lambda: `λ2x.t[x]` so_apply: `x[s]` sq_type: `SQType(T)` less_than: `a < b` squash: `↓T` less_than': `less_than'(a;b)` deq: `EqDecider(T)` bool: `𝔹` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` eqof: `eqof(d)` bfalse: `ff` bnot: `¬bb` assert: `↑b`
Lemmas referenced :  nat_properties satisfiable-full-omega-tt intformand_wf intformle_wf itermConstant_wf itermVar_wf intformless_wf int_formula_prop_and_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_wf ge_wf less_than_wf equal-wf-T-base nat_wf colength_wf_list less_than_transitivity1 less_than_irreflexivity list-cases list_ind_nil_lemma list_wf product_subtype_list spread_cons_lemma intformeq_wf itermAdd_wf int_formula_prop_eq_lemma int_term_value_add_lemma decidable__le intformnot_wf int_formula_prop_not_lemma le_wf equal_wf subtract_wf itermSubtract_wf int_term_value_subtract_lemma subtype_base_sq set_subtype_base int_subtype_base decidable__equal_int list_ind_cons_lemma bool_wf eqtt_to_assert safe-assert-deq append_wf unit_wf2 eqff_to_assert bool_cases_sqequal bool_subtype_base assert-bnot cons_wf deq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut thin lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination hypothesisEquality hypothesis setElimination rename sqequalRule intWeakElimination natural_numberEquality independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll independent_functionElimination axiomEquality equalityTransitivity equalitySymmetry because_Cache cumulativity applyEquality unionElimination inrEquality promote_hyp hypothesis_subsumption productElimination applyLambdaEquality dependent_set_memberEquality addEquality baseClosed instantiate imageElimination equalityElimination inlEquality universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[x:T].  \mforall{}[bs,checked:T  List].
(bag\_remove1\_aux(eq;checked;x;bs)  \mmember{}  T  List?)

Date html generated: 2018_05_21-PM-09_47_57
Last ObjectModification: 2017_07_26-PM-06_30_30

Theory : bags_2

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