Nuprl Lemma : bag-append-cancel
∀[T:Type]. ∀[as,bs,cs:bag(T)]. uiff((as + bs) = (as + cs) ∈ bag(T);bs = cs ∈ bag(T))
Proof
Definitions occuring in Statement :
bag-append: as + bs,
bag: bag(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
exists: ∃x:A. B[x],
prop: ℙ,
subtype_rel: A ⊆r B,
bag-append: as + bs,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bag: bag(T),
quotient: x,y:A//B[x; y],
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
bag_to_squash_list,
equal_wf,
bag_wf,
bag-append_wf,
list-subtype-bag,
and_wf,
list_induction,
append_wf,
list_wf,
list_ind_nil_lemma,
nil_wf,
cons_wf,
list_ind_cons_lemma,
cons_cancel_wrt_permutation,
quotient-member-eq,
permutation_wf,
permutation-equiv,
member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
cumulativity,
sqequalRule,
rename,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
equalityTransitivity,
dependent_set_memberEquality,
setElimination,
setEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
functionEquality,
independent_functionElimination,
lambdaFormation,
dependent_functionElimination,
voidElimination,
voidEquality,
pertypeElimination,
productEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs,cs:bag(T)]. uiff((as + bs) = (as + cs);bs = cs)
Date html generated:
2016_10_25-AM-10_21_57
Last ObjectModification:
2016_07_12-AM-06_38_54
Theory : bags
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