### Nuprl Lemma : concat-lifting2_wf

`∀[A,B,C:Type]. ∀[f:A ⟶ B ⟶ bag(C)]. ∀[abag:bag(A)]. ∀[bbag:bag(B)].  (concat-lifting2(f;abag;bbag) ∈ bag(C))`

Proof

Definitions occuring in Statement :  concat-lifting2: `concat-lifting2(f;abag;bbag)` bag: `bag(T)` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  concat-lifting2: `concat-lifting2(f;abag;bbag)` uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` int_seg: `{i..j-}` uimplies: `b supposing a` guard: `{T}` lelt: `i ≤ j < k` all: `∀x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` satisfiable_int_formula: `satisfiable_int_formula(fmla)` exists: `∃x:A. B[x]` top: `Top` sq_type: `SQType(T)` select: `L[n]` cons: `[a / b]` subtract: `n - m` funtype: `funtype(n;A;T)` eq_int: `(i =z j)` ifthenelse: `if b then t else f fi ` bfalse: `ff`
Lemmas referenced :  bag_wf primrec1_lemma primrec-unroll int_seg_cases int_seg_subtype int_subtype_base subtype_base_sq decidable__equal_int int_seg_wf int_term_value_add_lemma int_formula_prop_less_lemma itermAdd_wf intformless_wf decidable__lt length_of_nil_lemma length_of_cons_lemma int_formula_prop_wf int_term_value_var_lemma int_term_value_constant_lemma int_formula_prop_le_lemma int_formula_prop_not_lemma int_formula_prop_and_lemma itermVar_wf itermConstant_wf intformle_wf intformnot_wf intformand_wf satisfiable-full-omega-tt decidable__le int_seg_properties nil_wf cons_wf select_wf le_wf false_wf concat-lifting_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis lambdaEquality instantiate universeEquality because_Cache cumulativity setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality computeAll addEquality independent_functionElimination equalityTransitivity equalitySymmetry hypothesis_subsumption introduction functionEquality isect_memberFormation axiomEquality

Latex:
\mforall{}[A,B,C:Type].  \mforall{}[f:A  {}\mrightarrow{}  B  {}\mrightarrow{}  bag(C)].  \mforall{}[abag:bag(A)].  \mforall{}[bbag:bag(B)].
(concat-lifting2(f;abag;bbag)  \mmember{}  bag(C))

Date html generated: 2016_05_15-PM-03_07_26
Last ObjectModification: 2016_01_16-AM-08_34_58

Theory : bags

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