### Nuprl Lemma : concat-lifting-0_wf

`∀[B:Type]. ∀[f:bag(B)].  (concat-lifting-0(f) ∈ bag(B))`

Proof

Definitions occuring in Statement :  concat-lifting-0: `concat-lifting-0(f)` bag: `bag(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` concat-lifting-0: `concat-lifting-0(f)` select: `L[n]` uimplies: `b supposing a` all: `∀x:A. B[x]` nil: `[]` it: `⋅` so_lambda: `λ2x y.t[x; y]` top: `Top` so_apply: `x[s1;s2]` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` guard: `{T}` int_seg: `{i..j-}` lelt: `i ≤ j < k` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` subtype_rel: `A ⊆r B` funtype: `funtype(n;A;T)` concat-lifting: `concat-lifting(n;f;bags)` concat-lifting-list: `concat-lifting-list(n;bags)` bag-union: `bag-union(bbs)` concat: `concat(ll)` reduce: `reduce(f;k;as)` list_ind: list_ind lifting-gen-list-rev: `lifting-gen-list-rev(n;bags)` ifthenelse: `if b then t else f fi ` eq_int: `(i =z j)` btrue: `tt` single-bag: `{x}` cons: `[a / b]` append: `as @ bs`
Lemmas referenced :  bag_wf primrec0_lemma int_seg_wf int_formula_prop_wf int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_less_lemma int_formula_prop_and_lemma intformle_wf itermConstant_wf itermVar_wf intformless_wf intformand_wf satisfiable-full-omega-tt int_seg_properties le_wf false_wf concat-lifting_wf base_wf stuck-spread
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin baseClosed independent_isectElimination lambdaFormation hypothesis isect_memberEquality voidElimination voidEquality hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaEquality because_Cache setElimination rename productElimination dependent_pairFormation int_eqEquality intEquality dependent_functionElimination computeAll applyEquality axiomEquality equalityTransitivity equalitySymmetry universeEquality

Latex:
\mforall{}[B:Type].  \mforall{}[f:bag(B)].    (concat-lifting-0(f)  \mmember{}  bag(B))

Date html generated: 2016_05_15-PM-03_07_39
Last ObjectModification: 2016_01_16-AM-08_34_30

Theory : bags

Home Index