Nuprl Lemma : subtype_rel_bag
∀[B,A:Type]. bag(A) ⊆r bag(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
bag: bag(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
label: ...$L... t,
guard: {T},
prop: ℙ,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
cand: A c∧ B
Lemmas referenced :
bag_wf,
subtype_rel_wf,
list_wf,
quotient-member-eq,
permutation_wf,
permutation-equiv,
subtype_rel_list,
equal_wf,
equal-wf-base,
length_wf_nat,
nat_wf,
permute_list_wf,
int_seg_wf,
length_wf,
inject_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productElimination,
lambdaFormation,
rename,
independent_isectElimination,
dependent_functionElimination,
applyEquality,
independent_functionElimination,
productEquality,
dependent_pairFormation,
independent_pairFormation,
promote_hyp,
dependent_set_memberEquality,
hyp_replacement,
applyLambdaEquality,
setElimination,
functionExtensionality,
natural_numberEquality
Latex:
\mforall{}[B,A:Type]. bag(A) \msubseteq{}r bag(B) supposing A \msubseteq{}r B
Date html generated:
2017_10_01-AM-08_45_00
Last ObjectModification:
2017_07_26-PM-04_30_27
Theory : bags
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