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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