Nuprl Lemma : int-bag-sum_wf
∀[b:bag(ℤ)]. (Σ(b) ∈ ℤ)
Proof
Definitions occuring in Statement :
int-bag-sum: Σ(b),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-bag-sum: Σ(b),
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
assoc: Assoc(T;op),
infix_ap: x f y,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
comm: Comm(T;op)
Lemmas referenced :
bag_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
itermAdd_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
bag-summation_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
because_Cache,
lambdaEquality,
addEquality,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
hypothesis,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[b:bag(\mBbbZ{})]. (\mSigma{}(b) \mmember{} \mBbbZ{})
Date html generated:
2016_05_15-PM-02_33_25
Last ObjectModification:
2016_01_16-AM-08_53_12
Theory : bags
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