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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