Nuprl Lemma : mset_inj_wf_f
∀s:DSet. ∀x:|s|. (mset_inj{s}(x) ∈ FiniteSet{s})
Proof
Definitions occuring in Statement :
mset_inj: mset_inj{s}(x)
,
finite_set: FiniteSet{s}
,
all: ∀x:A. B[x]
,
member: t ∈ T
,
dset: DSet
,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x]
,
member: t ∈ T
,
finite_set: FiniteSet{s}
,
uall: ∀[x:A]. B[x]
,
subtype_rel: A ⊆r B
,
nat: ℕ
,
prop: ℙ
,
dset: DSet
,
mset_inj: mset_inj{s}(x)
,
mset_count: x #∈ a
,
mk_mset: mk_mset(as)
,
count: a #∈ as
,
so_lambda: λ2x.t[x]
,
top: Top
,
so_apply: x[s]
,
int_add_grp: <ℤ+>
,
grp_op: *
,
pi2: snd(t)
,
pi1: fst(t)
,
infix_ap: x f y
,
grp_id: e
,
b2i: b2i(b)
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
ifthenelse: if b then t else f fi
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
false: False
,
not: ¬A
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
,
rev_implies: P
⇐ Q
,
iff: P
⇐⇒ Q
Lemmas referenced :
mset_inj_wf,
le_wf,
mset_count_wf,
set_car_wf,
dset_wf,
mon_for_cons_lemma,
istype-void,
mon_for_nil_lemma,
set_eq_wf,
eqtt_to_assert,
assert_of_dset_eq,
istype-false,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
dependent_set_memberEquality_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
sqequalRule,
functionIsType,
universeIsType,
isectElimination,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
isect_memberEquality_alt,
voidElimination,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
independent_pairFormation,
dependent_pairFormation_alt,
equalityIsType1,
promote_hyp,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache
Latex:
\mforall{}s:DSet. \mforall{}x:|s|. (mset\_inj\{s\}(x) \mmember{} FiniteSet\{s\})
Date html generated:
2019_10_16-PM-01_06_54
Last ObjectModification:
2018_10_08-PM-00_08_36
Theory : mset
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