Nuprl Lemma : count_bounds
∀s:DSet. ∀a:|s|. ∀bs:|s| List. ((0 ≤ (a #∈ bs)) ∧ ((a #∈ bs) ≤ ||bs||))
Proof
Definitions occuring in Statement :
count: a #∈ as,
length: ||as||,
list: T List,
le: A ≤ B,
all: ∀x:A. B[x],
and: P ∧ Q,
natural_number: $n,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
dset: DSet,
so_apply: x[s],
implies: P ⇒ Q,
top: Top,
cand: A c∧ B,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
infix_ap: x f y,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Lemmas referenced :
list_induction,
le_wf,
count_wf,
length_wf,
set_car_wf,
list_wf,
count_nil_lemma,
length_of_nil_lemma,
count_cons_lemma,
length_of_cons_lemma,
dset_wf,
false_wf,
b2i_bounds,
set_eq_wf,
decidable__le,
b2i_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
productEquality,
natural_numberEquality,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
independent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
applyEquality,
productElimination,
addEquality,
unionElimination,
independent_isectElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality
Latex:
\mforall{}s:DSet. \mforall{}a:|s|. \mforall{}bs:|s| List. ((0 \mleq{} (a \#\mmember{} bs)) \mwedge{} ((a \#\mmember{} bs) \mleq{} ||bs||))
Date html generated:
2018_05_22-AM-07_45_23
Last ObjectModification:
2018_05_19-AM-08_32_32
Theory : list_2
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