Nuprl Lemma : sub-bag-size
∀[T:Type]. ∀[a,b:bag(T)]. #(a) ≤ #(b) supposing sub-bag(T;a;b)
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
bag-size: #(bs),
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sub-bag: sub-bag(T;as;bs),
exists: ∃x:A. B[x],
top: Top,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
guard: {T},
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
and: P ∧ Q,
subtype_rel: A ⊆r B,
le: A ≤ B
Lemmas referenced :
bag-size-append,
decidable__le,
bag-size_wf,
nat_properties,
set_wf,
le_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,
less_than'_wf,
sub-bag_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
sqequalRule,
extract_by_obid,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
because_Cache,
unionElimination,
cumulativity,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
intEquality,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
hyp_replacement,
Error :applyLambdaEquality,
independent_pairEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:bag(T)]. \#(a) \mleq{} \#(b) supposing sub-bag(T;a;b)
Date html generated:
2016_10_25-AM-10_38_06
Last ObjectModification:
2016_07_12-AM-06_51_45
Theory : bags
Home
Index