Nuprl Lemma : bag-no-repeats-subtype
∀[T,A:Type]. ∀[bs:bag(A)]. (bag-no-repeats(A;bs)) supposing (bag-no-repeats(T;bs) and strong-subtype(A;T))
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
strong-subtype: strong-subtype(A;B),
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,
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
bag: bag(T),
quotient: x,y:A//B[x; y],
permutation: permutation(T;L1;L2),
guard: {T}
Lemmas referenced :
bag-no-repeats_wf,
subtype_rel_bag,
strong-subtype_wf,
bag_wf,
list_wf,
equal_wf,
list-subtype-bag,
squash_wf,
exists_wf,
subtype_rel_list,
all_wf,
bag_to_squash_list,
sq_stable__all,
sq_stable__squash,
member_wf,
permutation_wf,
permute_list_wf,
int_seg_wf,
length_wf,
strong-subtype-list,
strong-subtype-implies,
no_repeats-subtype,
no_repeats_wf,
strong-subtype-bag
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
sqequalRule,
imageMemberEquality,
hypothesisEquality,
baseClosed,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
applyEquality,
independent_isectElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
lambdaEquality,
functionEquality,
lambdaFormation,
promote_hyp,
rename,
hyp_replacement,
applyLambdaEquality,
pertypeElimination,
productEquality,
dependent_pairFormation,
functionExtensionality,
natural_numberEquality,
independent_pairFormation,
dependent_set_memberEquality,
setElimination
Latex:
\mforall{}[T,A:Type]. \mforall{}[bs:bag(A)].
(bag-no-repeats(A;bs)) supposing (bag-no-repeats(T;bs) and strong-subtype(A;T))
Date html generated:
2017_10_01-AM-08_57_08
Last ObjectModification:
2017_07_26-PM-04_39_17
Theory : bags
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