Nuprl Lemma : single-valued-bag-append
∀[A:Type]. ∀[as,bs:bag(A)].
(single-valued-bag(as + bs;A)) supposing
(similar-bags(A;as;bs) and
single-valued-bag(as;A) and
single-valued-bag(bs;A))
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
similar-bags: similar-bags(A;as;bs),
bag-append: as + bs,
bag: bag(T),
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,
single-valued-bag: single-valued-bag(b;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
sq_or: a ↓∨ b,
squash: ↓T,
or: P ∨ Q,
similar-bags: similar-bags(A;as;bs),
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
false: False,
guard: {T},
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ,
cand: A c∧ B,
uiff: uiff(P;Q)
Lemmas referenced :
bag-member-append,
decidable__or,
equal-wf-base,
bag-size_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
less_than_wf,
decidable__equal_int,
decidable__lt,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
intformor_wf,
intformeq_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_or_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
bag-member_wf,
bag-append_wf,
similar-bags_wf,
single-valued-bag_wf,
bag_wf,
istype-universe,
bag-size-zero,
decidable__le,
bag-member-empty-iff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation_alt,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
productElimination,
independent_functionElimination,
imageElimination,
unionElimination,
sqequalRule,
intEquality,
applyEquality,
lambdaEquality_alt,
natural_numberEquality,
independent_isectElimination,
baseClosed,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
applyLambdaEquality,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
axiomEquality,
functionIsTypeImplies,
isect_memberEquality_alt,
isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as,bs:bag(A)].
(single-valued-bag(as + bs;A)) supposing
(similar-bags(A;as;bs) and
single-valued-bag(as;A) and
single-valued-bag(bs;A))
Date html generated:
2020_05_20-AM-08_01_57
Last ObjectModification:
2020_01_10-PM-03_01_29
Theory : bags
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