### Nuprl Lemma : concat-lifting-list_wf

`∀[B:Type]. ∀[n:ℕ]. ∀[m:ℕn + 1]. ∀[A:ℕn ⟶ Type]. ∀[bags:k:ℕn ⟶ bag(A k)]. ∀[g:funtype(n - m;λx.(A (x + m));bag(B))].`
`  (concat-lifting-list(n;bags) m g ∈ bag(B))`

Proof

Definitions occuring in Statement :  concat-lifting-list: `concat-lifting-list(n;bags)` bag: `bag(T)` funtype: `funtype(n;A;T)` int_seg: `{i..j-}` nat: `ℕ` uall: `∀[x:A]. B[x]` member: `t ∈ T` apply: `f a` lambda: `λx.A[x]` function: `x:A ⟶ B[x]` subtract: `n - m` add: `n + m` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  concat-lifting-list: `concat-lifting-list(n;bags)` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` int_seg: `{i..j-}` guard: `{T}` ge: `i ≥ j ` lelt: `i ≤ j < k` and: `P ∧ Q` 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]` false: `False` implies: `P `` Q` not: `¬A` top: `Top` prop: `ℙ` uiff: `uiff(P;Q)` le: `A ≤ B` less_than: `a < b`
Lemmas referenced :  nat_wf int_seg_wf lelt_wf decidable__lt add-member-int_seg1 le_wf int_formula_prop_wf int_term_value_add_lemma int_formula_prop_less_lemma int_term_value_var_lemma int_term_value_subtract_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermAdd_wf intformless_wf itermVar_wf itermSubtract_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le nat_properties int_seg_properties subtract_wf funtype_wf bag_wf lifting-gen-list-rev_wf bag-union_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity sqequalRule cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis cumulativity dependent_set_memberEquality setElimination rename natural_numberEquality addEquality productElimination dependent_functionElimination unionElimination independent_isectElimination dependent_pairFormation lambdaEquality int_eqEquality intEquality isect_memberEquality voidElimination voidEquality independent_pairFormation computeAll applyEquality because_Cache functionEquality universeEquality isect_memberFormation introduction axiomEquality equalityTransitivity equalitySymmetry

Latex:
\mforall{}[B:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[m:\mBbbN{}n  +  1].  \mforall{}[A:\mBbbN{}n  {}\mrightarrow{}  Type].  \mforall{}[bags:k:\mBbbN{}n  {}\mrightarrow{}  bag(A  k)].
\mforall{}[g:funtype(n  -  m;\mlambda{}x.(A  (x  +  m));bag(B))].
(concat-lifting-list(n;bags)  m  g  \mmember{}  bag(B))

Date html generated: 2016_05_15-PM-03_05_29
Last ObjectModification: 2016_01_16-AM-08_34_51

Theory : bags

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