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: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r 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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