Nuprl Lemma : mset_diff_wf_f
∀s:DSet. ∀a,b:FiniteSet{s}. (a - b ∈ FiniteSet{s})
Proof
Definitions occuring in Statement :
mset_diff: a - b,
finite_set: FiniteSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
guard: {T},
finite_set: FiniteSet{s},
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s],
prop: ℙ,
squash: ↓T,
true: True,
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
ndiff: a -- b,
le: A ≤ B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
less_than': less_than'(a;b),
false: False,
not: ¬A,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
decidable: Dec(P),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top
Lemmas referenced :
finite_set_wf,
dset_wf,
fset_properties,
mset_diff_wf,
set_car_wf,
all_wf,
le_wf,
mset_count_wf,
nat_wf,
squash_wf,
true_wf,
mset_count_diff,
iff_weakening_equal,
imax_unfold,
subtract_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
false_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
decidable__le,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalHypSubstitution,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
setElimination,
rename,
dependent_set_memberEquality,
because_Cache,
sqequalRule,
lambdaEquality,
applyEquality,
natural_numberEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
unionElimination,
equalityElimination,
independent_pairFormation,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
applyLambdaEquality,
int_eqEquality,
isect_memberEquality,
voidEquality,
computeAll
Latex:
\mforall{}s:DSet. \mforall{}a,b:FiniteSet\{s\}. (a - b \mmember{} FiniteSet\{s\})
Date html generated:
2017_10_01-AM-10_00_28
Last ObjectModification:
2017_03_03-PM-01_01_47
Theory : mset
Home
Index