Nuprl Lemma : fset-item_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. item(s) ∈ T supposing ||s|| = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
fset-item: item(s),
fset-size: ||s||,
fset: fset(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fset: fset(T),
all: ∀x:A. B[x],
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
fset-size: ||s||,
fset-item: item(s),
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
ge: i ≥ j ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
listp: A List+
Lemmas referenced :
list_wf,
set-equal_wf,
set-equal-reflex,
length-remove-repeats-le,
decidable__le,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
hd_wf,
member_wf,
squash_wf,
true_wf,
fset-size_wf,
set_subtype_base,
le_wf,
int_subtype_base,
fset_wf,
deq_wf,
istype-universe,
list-cases,
length_of_nil_lemma,
istype-le,
nil_wf,
product_subtype_list,
length_of_cons_lemma,
cons_wf,
cons_member,
l_member_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
btrue_neq_bfalse,
non_neg_length,
itermAdd_wf,
int_term_value_add_lemma,
length-one-iff,
remove-repeats_wf,
member-remove-repeats,
hd_member,
listp-not-nil,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-less_than,
iff_weakening_uiff,
assert_wf,
null_wf,
equal-wf-T-base,
assert_of_null,
istype-assert
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
Error :universeIsType,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
promote_hyp,
Error :lambdaFormation_alt,
Error :inhabitedIsType,
pointwiseFunctionality,
sqequalRule,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :productIsType,
Error :equalityIsType4,
applyEquality,
imageElimination,
because_Cache,
imageMemberEquality,
baseClosed,
axiomEquality,
Error :equalityIstype,
intEquality,
closedConclusion,
sqequalBase,
Error :isectIsTypeImplies,
instantiate,
universeEquality,
Error :equalityIsType1,
hypothesis_subsumption,
rename,
Error :inlFormation_alt,
addEquality,
Error :dependent_set_memberEquality_alt
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. item(s) \mmember{} T supposing ||s|| = 1
Date html generated:
2019_06_20-PM-02_00_05
Last ObjectModification:
2018_11_23-PM-02_42_42
Theory : finite!sets
Home
Index