Nuprl Lemma : bag-no-repeats-supertype
∀[T,S:Type]. ∀[bs:bag(S)]. bag-no-repeats(T;bs) supposing strong-subtype(S;T) ∧ bag-no-repeats(S;bs)
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],
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
bag-no-repeats: bag-no-repeats(T;bs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
squash: ↓T,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
strong-subtype: strong-subtype(A;B),
cand: A c∧ B,
guard: {T},
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
subtype_rel_list,
subtype_rel_bag,
equal_functionality_wrt_subtype_rel2,
bag_wf,
no_repeats-strong-subtype,
equal_wf,
list-subtype-bag,
no_repeats_wf,
strong-subtype_wf,
squash_wf,
exists_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
imageElimination,
dependent_pairFormation,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
independent_isectElimination,
hypothesis,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
independent_pairFormation,
because_Cache,
productEquality,
lambdaEquality,
imageMemberEquality,
baseClosed,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T,S:Type]. \mforall{}[bs:bag(S)].
bag-no-repeats(T;bs) supposing strong-subtype(S;T) \mwedge{} bag-no-repeats(S;bs)
Date html generated:
2018_05_21-PM-09_53_02
Last ObjectModification:
2017_07_26-PM-06_32_15
Theory : bags_2
Home
Index