Nuprl Lemma : bag-subtract-append
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. (bag-subtract(eq;as + bs;as) = bs ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-subtract: bag-subtract(eq;bs;as),
bag-append: as + bs,
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
bag-subtract: bag-subtract(eq;bs;as),
all: ∀x:A. B[x],
bag-accum: bag-accum(v,x.f[v; x];init;bs),
list_accum: list_accum,
nil: [],
it: ⋅,
bag-append: as + bs,
append: as @ bs,
list_ind: list_ind,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bag_to_squash_list,
list_induction,
all_wf,
list_wf,
equal_wf,
bag_wf,
bag-subtract_wf,
bag-append_wf,
list-subtype-bag,
list_accum_cons_lemma,
list_ind_cons_lemma,
bag-drop-head,
append_wf,
squash_wf,
true_wf,
iff_weakening_equal,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
rename,
sqequalRule,
lambdaEquality,
cumulativity,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
hyp_replacement,
applyLambdaEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:bag(T)]. (bag-subtract(eq;as + bs;as) = bs)
Date html generated:
2018_05_21-PM-09_49_25
Last ObjectModification:
2017_07_26-PM-06_31_03
Theory : bags_2
Home
Index