Nuprl Lemma : bag-cases
∀[T:Type]. ∀bs:bag(T). ((bs = {} ∈ bag(T)) ∨ (↓∃x:T. ∃bs':bag(T). (bs = ({x} + bs') ∈ bag(T))))
Proof
Definitions occuring in Statement :
bag-append: as + bs,
single-bag: {x},
empty-bag: {},
bag: bag(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
squash: ↓T,
exists: ∃x:A. B[x],
bag-size: #(bs),
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
false: False,
cons: [a / b],
single-bag: {x},
bag-append: as + bs,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3]
Lemmas referenced :
decidable__le,
bag-size_wf,
nat_wf,
bag-size-zero,
empty-bag_wf,
squash_wf,
exists_wf,
bag_wf,
equal_wf,
bag-append_wf,
single-bag_wf,
bag_to_squash_list,
not_wf,
le_wf,
list-cases,
length_of_nil_lemma,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
product_subtype_list,
length_of_cons_lemma,
list-subtype-bag,
list_ind_cons_lemma,
list_ind_nil_lemma,
cons_wf,
equal-wf-T-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
natural_numberEquality,
unionElimination,
inlFormation,
independent_isectElimination,
inrFormation,
imageElimination,
productElimination,
promote_hyp,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
because_Cache,
dependent_pairFormation,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
hypothesis_subsumption,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}bs:bag(T). ((bs = \{\}) \mvee{} (\mdownarrow{}\mexists{}x:T. \mexists{}bs':bag(T). (bs = (\{x\} + bs'))))
Date html generated:
2016_10_25-AM-10_22_26
Last ObjectModification:
2016_07_12-AM-06_39_07
Theory : bags
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