### Nuprl Lemma : lifting2_wf

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

Proof

Definitions occuring in Statement :  lifting2: `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 :  uall: `∀[x:A]. B[x]` member: `t ∈ T` lifting2: `lifting2(f;abag;bbag)` 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` subtype_rel: `A ⊆r B` funtype: `funtype(n;A;T)` primrec: `primrec(n;b;c)`
Lemmas referenced :  lifting-gen-rev_wf false_wf le_wf select_wf cons_wf nil_wf int_seg_properties decidable__le full-omega-unsat intformand_wf intformnot_wf intformle_wf itermConstant_wf itermVar_wf int_formula_prop_and_lemma int_formula_prop_not_lemma int_formula_prop_le_lemma int_term_value_constant_lemma int_term_value_var_lemma int_formula_prop_wf length_of_cons_lemma length_of_nil_lemma decidable__lt intformless_wf itermAdd_wf int_formula_prop_less_lemma int_term_value_add_lemma int_seg_wf decidable__equal_int subtype_base_sq int_subtype_base int_seg_subtype int_seg_cases subtype_rel_self funtype_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation hypothesis lambdaEquality instantiate universeEquality because_Cache cumulativity setElimination rename independent_isectElimination productElimination dependent_functionElimination unionElimination approximateComputation independent_functionElimination dependent_pairFormation int_eqEquality intEquality isect_memberEquality voidElimination voidEquality addEquality equalityTransitivity equalitySymmetry hypothesis_subsumption applyEquality axiomEquality functionEquality

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

Date html generated: 2018_05_21-PM-06_26_19
Last ObjectModification: 2018_05_19-PM-05_15_57

Theory : bags

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