Nuprl Lemma : bag-size-cons
∀[b:bag(Top)]. ∀[x:Top]. (#(x.b) ~ 1 + #(b))
Proof
Definitions occuring in Statement :
bag-size: #(bs),
cons-bag: x.b,
bag: bag(T),
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
nat: ℕ,
subtype_rel: A ⊆r B,
guard: {T},
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
bag-size: #(bs),
cons-bag: x.b,
uiff: uiff(P;Q),
le: A ≤ B,
less_than': less_than'(a;b),
sq_type: SQType(T)
Lemmas referenced :
bag-size_wf,
top_wf,
cons-bag_wf,
nat_properties,
decidable__le,
nat_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
itermAdd_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_term_value_add_lemma,
int_formula_prop_wf,
le_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
length_of_cons_lemma,
decidable__equal_int,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
false_wf,
add_nat_wf,
equal_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
natural_numberEquality,
applyEquality,
because_Cache,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
dependent_functionElimination,
lambdaEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
instantiate,
cumulativity,
pointwiseFunctionality,
promote_hyp,
baseClosed,
baseApply,
closedConclusion,
productElimination,
lambdaFormation,
independent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[b:bag(Top)]. \mforall{}[x:Top]. (\#(x.b) \msim{} 1 + \#(b))
Date html generated:
2017_10_01-AM-08_45_46
Last ObjectModification:
2017_07_26-PM-04_30_54
Theory : bags
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