Nuprl Lemma : bag-subtract-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs,as:bag(T)]. bag-no-repeats(T;bag-subtract(eq;bs;as)) supposing bag-no-repeats(T;bs)
Proof
Definitions occuring in Statement :
bag-subtract: bag-subtract(eq;bs;as),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-no-repeats: bag-no-repeats(T;bs),
squash: ↓T,
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
bag-subtract: bag-subtract(eq;bs;as),
bag-accum: bag-accum(v,x.f[v; x];init;bs),
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
or: P ∨ Q,
and: P ∧ Q,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q)
Lemmas referenced :
bag-no-repeats_wf,
bag_wf,
deq_wf,
bag-subtract_wf,
squash_wf,
all_wf,
bag_to_squash_list,
sq_stable__all,
sq_stable__bag-no-repeats,
list_induction,
list-subtype-bag,
list_wf,
list_accum_nil_lemma,
list_accum_cons_lemma,
bag-drop_wf,
bag-drop-property,
true_wf,
iff_weakening_equal,
bag-no-repeats-append,
single-bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
imageElimination,
hypothesis,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
extract_by_obid,
isectElimination,
cumulativity,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
lambdaEquality,
functionEquality,
lambdaFormation,
productElimination,
promote_hyp,
rename,
applyEquality,
independent_isectElimination,
hyp_replacement,
Error :applyLambdaEquality,
voidElimination,
voidEquality,
unionElimination,
natural_numberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs,as:bag(T)].
bag-no-repeats(T;bag-subtract(eq;bs;as)) supposing bag-no-repeats(T;bs)
Date html generated:
2016_10_25-AM-11_28_25
Last ObjectModification:
2016_07_12-AM-07_34_44
Theory : bags_2
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