Nuprl Lemma : bag-size-bound
∀[T:Type]. ∀[as,bs:bag(T)]. ∀[n:ℕ]. #(as + bs) - n < #(bs) supposing #(as) < n
Proof
Definitions occuring in Statement :
bag-size: #(bs),
bag-append: as + bs,
bag: bag(T),
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
subtract: n - m,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ
Lemmas referenced :
bag_wf,
bag-append_wf,
member-less_than,
nat_wf,
less_than_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermSubtract_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
bag-size_wf,
subtract_wf,
decidable__lt,
nat_properties,
bag-size-append
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
setElimination,
rename,
dependent_functionElimination,
addEquality,
applyEquality,
because_Cache,
unionElimination,
imageElimination,
productElimination,
lambdaEquality,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)]. \mforall{}[n:\mBbbN{}]. \#(as + bs) - n < \#(bs) supposing \#(as) < n
Date html generated:
2016_05_15-PM-02_25_12
Last ObjectModification:
2016_01_16-AM-08_57_03
Theory : bags
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