Nuprl Lemma : mset_fact
∀s:DSet. ∀a:MSet{s}. (a = (msFor{mset_mon{s}} x ∈ a. mset_inj{s}(x)) ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_for: mset_for,
mset_mon: mset_mon{s},
mset_inj: mset_inj{s}(x),
mset: MSet{s},
all: ∀x:A. B[x],
equal: s = t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
mon: Mon,
imon: IMonoid,
uall: ∀[x:A]. B[x],
dset: DSet,
so_lambda: λ2x.t[x],
list: T List,
grp_car: |g|,
pi1: fst(t),
lapp_mon: <s List, @>,
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
mset: MSet{s},
quotient: x,y:A//B[x; y],
mset_mon: mset_mon{s},
guard: {T},
uimplies: b supposing a,
ge: i ≥ j ,
top: Top,
decidable: Dec(P),
or: P ∨ Q,
false: False,
le: A ≤ B,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
b2i: b2i(b),
ifthenelse: if b then t else f fi ,
infix_ap: x f y,
set_eq: =b,
pi2: snd(t),
count: a #∈ as,
mon_for: For{g} x ∈ as. f[x],
for: For{T,op,id} x ∈ as. f[x],
reduce: reduce(f;k;as),
list_ind: list_ind,
map: map(f;as),
cons: [a / b],
grp_op: *,
int_add_grp: <ℤ+>,
tlambda: λx:T. b[x],
nil: [],
it: ⋅,
grp_id: e,
prop: ℙ,
dislist: DisList{s},
mk_mset: mk_mset(as),
mset_inj: mset_inj{s}(x),
squash: ↓T,
true: True
Lemmas referenced :
dset_wf,
equal_mset_elim,
mon_for_wf,
lapp_mon_wf,
subtype_rel_self,
imon_wf,
set_car_wf,
cons_wf,
nil_wf,
grp_car_wf,
mon_subtype_grp_sig,
list_wf,
iff_transitivity,
all_wf,
mset_wf,
equal_wf,
mset_for_wf,
mset_mon_wf,
abmonoid_subtype_iabmonoid,
mset_inj_wf,
abmonoid_subtype_mon,
subtype_rel_transitivity,
abmonoid_wf,
mon_wf,
grp_sig_wf,
mk_mset_wf,
mk_mset_wf2,
length_nil,
non_neg_length,
length_cons,
count_bounds,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
count_cons_lemma,
count_nil_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
le_wf,
count_wf,
all_mset_elim,
sq_stable__equal,
mset_for_elim_lemma,
squash_wf,
true_wf,
mset_mon_for_elim,
iff_weakening_equal,
permr_wf,
permr_weakening,
lapp_fact
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
addLevel,
allFunctionality,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
instantiate,
isectElimination,
setElimination,
rename,
lambdaEquality,
because_Cache,
productElimination,
independent_functionElimination,
independent_isectElimination,
voidEquality,
isect_memberEquality,
voidElimination,
unionElimination,
natural_numberEquality,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
levelHypothesis,
imageElimination,
functionEquality,
cumulativity,
universeEquality,
imageMemberEquality,
baseClosed,
allLevelFunctionality
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. (a = (msFor\{mset\_mon\{s\}\} x \mmember{} a. mset\_inj\{s\}(x)))
Date html generated:
2018_05_22-AM-07_45_46
Last ObjectModification:
2018_05_19-AM-08_30_47
Theory : mset
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