Nuprl Lemma : fset_of_mset_count_bound
∀s:DSet. ∀a:MSet{s}. ∀c:|s|. ((c #∈ fset_of_mset(s;a)) ≤ 1)
Proof
Definitions occuring in Statement :
fset_of_mset: fset_of_mset(s;a),
mset_count: x #∈ a,
mset: MSet{s},
le: A ≤ B,
all: ∀x:A. B[x],
natural_number: $n,
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
dset: DSet,
nat: ℕ,
fset_of_mset: fset_of_mset(s;a),
top: Top,
mset_union_mon: <MSet{s},⋃,0>,
grp_id: e,
pi2: snd(t),
pi1: fst(t),
null_mset: 0{s},
mset_count: x #∈ a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
squash: ↓T,
grp_car: |g|,
mset: MSet{s},
quotient: x,y:A//B[x; y],
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
mset_inj: mset_inj{s}(x),
mk_mset: mk_mset(as),
infix_ap: x f y,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
grp_op: *,
uiff: uiff(P;Q),
cand: A c∧ B
Lemmas referenced :
mset_ind_a,
le_wf,
mset_count_wf,
fset_of_mset_wf,
mset_wf,
set_car_wf,
dset_wf,
sq_stable__le,
mset_for_null_lemma,
istype-void,
count_nil_lemma,
istype-false,
squash_wf,
true_wf,
istype-int,
mset_for_mset_inj,
mset_union_mon_wf,
abmonoid_subtype_iabmonoid,
mset_inj_wf,
subtype_rel_self,
nat_wf,
iff_weakening_equal,
count_cons_lemma,
b2i_bounds,
set_eq_wf,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
mset_for_mset_sum,
mset_count_union,
imax_lb
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
isectElimination,
because_Cache,
hypothesis,
applyEquality,
natural_numberEquality,
universeIsType,
independent_functionElimination,
inhabitedIsType,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
imageElimination,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
unionElimination,
approximateComputation,
dependent_pairFormation_alt,
int_eqEquality
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. \mforall{}c:|s|. ((c \#\mmember{} fset\_of\_mset(s;a)) \mleq{} 1)
Date html generated:
2019_10_16-PM-01_06_45
Last ObjectModification:
2018_10_08-PM-05_41_01
Theory : mset
Home
Index