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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