### Nuprl Lemma : concat-lifting-gen_wf

`∀[B:Type]. ∀[n:ℕ]. ∀[A:ℕn ⟶ Type]. ∀[f:funtype(n;A;bag(B))].  (concat-lifting-gen(n;f) ∈ (k:ℕn ⟶ bag(A k)) ⟶ bag(B))`

Proof

Definitions occuring in Statement :  concat-lifting-gen: `concat-lifting-gen(n;f)` 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` function: `x:A ⟶ B[x]` natural_number: `\$n` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` concat-lifting-gen: `concat-lifting-gen(n;f)` nat: `ℕ`
Lemmas referenced :  concat-lifting_wf int_seg_wf bag_wf funtype_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lambdaEquality lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis functionEquality natural_numberEquality setElimination rename applyEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache cumulativity universeEquality

Latex:
\mforall{}[B:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[A:\mBbbN{}n  {}\mrightarrow{}  Type].  \mforall{}[f:funtype(n;A;bag(B))].
(concat-lifting-gen(n;f)  \mmember{}  (k:\mBbbN{}n  {}\mrightarrow{}  bag(A  k))  {}\mrightarrow{}  bag(B))

Date html generated: 2016_05_15-PM-03_07_01
Last ObjectModification: 2015_12_27-AM-09_27_02

Theory : bags

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