Nuprl Lemma : bag-splits-permutation
∀T:Type. ∀L1,L2:T List. (permutation(T;L1;L2) ⇒ permutation(bag(T) × bag(T);bag-splits(L1);bag-splits(L2)))
Proof
Definitions occuring in Statement :
bag-splits: bag-splits(b),
bag: bag(T),
permutation: permutation(T;L1;L2),
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
trans: Trans(T;x,y.E[x; y]),
guard: {T},
prop: ℙ,
refl: Refl(T;x,y.E[x; y]),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bag-splits: bag-splits(b),
bag-append: as + bs,
bag-map: bag-map(f;bs)
Lemmas referenced :
permutation-invariant2,
permutation_wf,
bag_wf,
bag-splits_wf_list,
list_wf,
permutation_transitivity,
permutation_weakening,
bag-splits-permutation1,
list_induction,
cons_wf,
append_wf,
nil_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
equal_wf,
append_functionality_wrt_permutation,
map_wf,
bag-append_wf,
single-bag_wf,
pi1_wf,
pi2_wf,
permutation-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality,
productEquality,
cumulativity,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
independent_isectElimination,
universeEquality,
promote_hyp,
rename,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairEquality,
productElimination
Latex:
\mforall{}T:Type. \mforall{}L1,L2:T List.
(permutation(T;L1;L2) {}\mRightarrow{} permutation(bag(T) \mtimes{} bag(T);bag-splits(L1);bag-splits(L2)))
Date html generated:
2017_10_01-AM-09_00_01
Last ObjectModification:
2017_07_26-PM-04_42_01
Theory : bags
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