Nuprl Lemma : sub-bags-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)].  bag-no-repeats(bag(T);sub-bags(eq;bs)) supposing valueall-type(T)
Proof
Definitions occuring in Statement : 
sub-bags: sub-bags(eq;bs)
, 
bag-no-repeats: bag-no-repeats(T;bs)
, 
bag: bag(T)
, 
deq: EqDecider(T)
, 
valueall-type: valueall-type(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
, 
sub-bags: sub-bags(eq;bs)
, 
bag-no-repeats: bag-no-repeats(T;bs)
, 
squash: ↓T
, 
all: ∀x:A. B[x]
, 
prop: ℙ
, 
implies: P 
⇒ Q
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
top: Top
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
inject: Inj(A;B;f)
, 
pi1: fst(t)
, 
rev_uimplies: rev_uimplies(P;Q)
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
valueall-type_wf, 
bag_wf, 
deq_wf, 
bag-subtype, 
bag-partitions_wf, 
bag-member_wf, 
equal_wf, 
bag-map-no-repeats, 
pi1_wf_top, 
subtype_rel_product, 
top_wf, 
set_wf, 
bag-member-partitions, 
and_wf, 
bag-append_wf, 
bag-append-cancel, 
bag-no-repeats_wf, 
subtype_rel_bag, 
no-repeats-bag-partitions, 
bag-no-repeats-settype, 
decidable__equal_product, 
decidable__equal_bag, 
decidable-equal-deq, 
squash_wf, 
true_wf, 
iff_weakening_equal
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, 
productEquality, 
dependent_functionElimination, 
independent_isectElimination, 
setEquality, 
productElimination, 
independent_pairEquality, 
lambdaFormation, 
independent_functionElimination, 
lambdaEquality, 
setElimination, 
rename, 
applyEquality, 
voidElimination, 
voidEquality, 
dependent_set_memberEquality, 
independent_pairFormation, 
applyLambdaEquality, 
hyp_replacement, 
instantiate, 
natural_numberEquality
Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[bs:bag(T)].
    bag-no-repeats(bag(T);sub-bags(eq;bs))  supposing  valueall-type(T)
Date html generated:
2018_05_21-PM-09_52_37
Last ObjectModification:
2017_07_26-PM-06_31_54
Theory : bags_2
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