Nuprl Lemma : mset_sum_bor_mon_hom
∀s:DSet. ∀x:|s|. IsMonHom{mset_mon{s},<𝔹,∨b>}(λu.(x ∈b u))
Proof
Definitions occuring in Statement :
mset_mem: mset_mem,
mset_mon: mset_mon{s},
all: ∀x:A. B[x],
lambda: λx.A[x],
bor_mon: <𝔹,∨b>,
monoid_hom_p: IsMonHom{M1,M2}(f),
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
mset_mon: mset_mon{s},
grp_car: |g|,
pi1: fst(t),
bor_mon: <𝔹,∨b>,
grp_op: *,
pi2: snd(t),
grp_id: e,
infix_ap: x f y,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
dset: DSet,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
nat: ℕ,
gt: i > j,
or: P ∨ Q,
uiff: uiff(P;Q),
squash: ↓T,
true: True,
guard: {T},
decidable: Dec(P),
false: False,
less_than: a < b,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
ge: i ≥ j
Lemmas referenced :
bfalse_wf,
int_formula_prop_le_lemma,
intformle_wf,
le_wf,
nat_properties,
false_wf,
int_formula_prop_wf,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_or_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformor_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
add-is-int-iff,
decidable__lt,
less_than_wf,
decidable__or,
iff_weakening_equal,
mset_count_sum,
true_wf,
squash_wf,
assert_of_bor,
or_wf,
iff_wf,
nat_wf,
mset_count_wf,
gt_wf,
assert_wf,
mset_mem_iff_count_nzero,
bor_wf,
mset_sum_wf,
mset_mem_wf,
iff_imp_equal_bool,
dset_wf,
set_car_wf,
mset_wf,
mset_mem_null_lemma
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation,
independent_pairFormation,
isect_memberFormation,
introduction,
hypothesisEquality,
isectElimination,
axiomEquality,
because_Cache,
setElimination,
rename,
independent_isectElimination,
addLevel,
productElimination,
impliesFunctionality,
independent_functionElimination,
orFunctionality,
applyEquality,
lambdaEquality,
natural_numberEquality,
orLevelFunctionality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
imageMemberEquality,
baseClosed,
unionElimination,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
dependent_pairFormation,
int_eqEquality,
computeAll,
addEquality,
setEquality
Latex:
\mforall{}s:DSet. \mforall{}x:|s|. IsMonHom\{mset\_mon\{s\},<\mBbbB{},\mvee{}\msubb{}>\}(\mlambda{}u.(x \mmember{}\msubb{} u))
Date html generated:
2016_05_16-AM-07_49_54
Last ObjectModification:
2016_01_16-PM-11_39_51
Theory : mset
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