### Nuprl Lemma : lifting1_wf

[A,B:Type]. ∀[f:A ⟶ B]. ∀[b:bag(A)].  (lifting1(f;b) ∈ bag(B))

Proof

Definitions occuring in Statement :  lifting1: lifting1(f;b) 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 lifting1: lifting1(f;b) nat: le: A ≤ B and: P ∧ Q less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: subtype_rel: A ⊆B funtype: funtype(n;A;T) all: x:A. B[x] top: Top
Lemmas referenced :  lifting-gen-rev_wf false_wf le_wf int_seg_wf primrec1_lemma subtype_rel_self bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_set_memberEquality natural_numberEquality independent_pairFormation lambdaFormation hypothesis lambdaEquality applyEquality dependent_functionElimination isect_memberEquality voidElimination voidEquality because_Cache equalityTransitivity equalitySymmetry axiomEquality functionEquality universeEquality

Latex:
\mforall{}[A,B:Type].  \mforall{}[f:A  {}\mrightarrow{}  B].  \mforall{}[b:bag(A)].    (lifting1(f;b)  \mmember{}  bag(B))

Date html generated: 2016_05_15-PM-03_00_53
Last ObjectModification: 2015_12_27-AM-09_28_54

Theory : bags

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