Nuprl Lemma : int-bag-sum-append
∀[b1,b2:bag(ℤ)]. (Σ(b1 + b2) ~ Σ(b1) + Σ(b2))
Proof
Definitions occuring in Statement :
int-bag-sum: Σ(b),
bag-append: as + bs,
bag: bag(T),
uall: ∀[x:A]. B[x],
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
int-bag-sum: Σ(b),
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T},
monoid_p: IsMonoid(T;op;id),
and: P ∧ Q,
assoc: Assoc(T;op),
infix_ap: x f y,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
ident: Ident(T;op;id),
cand: A c∧ B,
comm: Comm(T;op),
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
squash: ↓T,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
bag_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
itermConstant_wf,
int_term_value_constant_lemma,
bag-summation_wf,
equal_wf,
squash_wf,
true_wf,
bag-summation-append,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
sqequalRule,
isect_memberEquality,
hypothesisEquality,
because_Cache,
independent_pairFormation,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
productElimination,
independent_pairEquality,
addEquality,
applyEquality,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[b1,b2:bag(\mBbbZ{})]. (\mSigma{}(b1 + b2) \msim{} \mSigma{}(b1) + \mSigma{}(b2))
Date html generated:
2017_10_01-AM-08_51_44
Last ObjectModification:
2017_07_26-PM-04_33_28
Theory : bags
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