Nuprl Lemma : mset_union_ident_l
∀s:DSet. ∀a:MSet{s}. ((0{s} ⋃ a) = a ∈ MSet{s})
Proof
Definitions occuring in Statement :
mset_union: a ⋃ b,
null_mset: 0{s},
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
dset: DSet,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
true: True,
so_apply: x[s],
uimplies: b supposing a,
guard: {T},
null_mset: 0{s},
mset_count: x #∈ a,
top: Top,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
decidable: Dec(P),
or: P ∨ Q,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A
Lemmas referenced :
eq_mset_iff_eq_counts,
mset_union_wf,
null_mset_wf,
all_wf,
squash_wf,
true_wf,
set_car_wf,
equal_wf,
mset_count_union,
mset_count_wf,
nat_wf,
iff_weakening_equal,
mset_wf,
dset_wf,
count_nil_lemma,
imax_unfold,
le_int_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
le_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
less_than_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
decidable__equal_int,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
setElimination,
rename,
sqequalRule,
because_Cache,
intEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
unionElimination,
equalityElimination,
applyLambdaEquality,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}s:DSet. \mforall{}a:MSet\{s\}. ((0\{s\} \mcup{} a) = a)
Date html generated:
2017_10_01-AM-09_59_56
Last ObjectModification:
2017_03_03-PM-01_00_56
Theory : mset
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