Nuprl Lemma : bag-size-is-zero
∀[C:Type]. ∀[bs:bag(C)]. bs ~ {} supposing #(bs) = 0 ∈ ℤ
Proof
Definitions occuring in Statement :
bag-size: #(bs),
empty-bag: {},
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n,
int: ℤ,
universe: Type,
sqequal: s ~ t,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
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,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
bag_wf,
nat_wf,
bag-size_wf,
equal_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
bag-size-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
sqequalAxiom,
applyEquality,
setElimination,
rename,
because_Cache,
universeEquality
Latex:
\mforall{}[C:Type]. \mforall{}[bs:bag(C)]. bs \msim{} \{\} supposing \#(bs) = 0
Date html generated:
2016_05_15-PM-02_25_10
Last ObjectModification:
2016_01_16-AM-08_56_58
Theory : bags
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