Nuprl Lemma : single-valued-bag-if-le1
∀[T:Type]. ∀[b:bag(T)]. single-valued-bag(b;T) supposing #(b) ≤ 1
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
bag-size: #(bs),
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
single-valued-bag: single-valued-bag(b;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
guard: {T},
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
squash: ↓T,
bag-size: #(bs),
uiff: uiff(P;Q),
empty-bag: {},
true: True,
iff: P ⇐⇒ Q,
single-bag: {x}
Lemmas referenced :
decidable__or,
equal-wf-T-base,
bag-size_wf,
decidable__equal_int,
nat_properties,
set_wf,
le_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
intformor_wf,
intformeq_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_formula_prop_or_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
bag_to_squash_list,
or_wf,
bag-member_wf,
nat_wf,
bag_wf,
length_zero,
length_wf_nat,
equal_wf,
subtype_rel_set,
list_wf,
list-subtype-bag,
bag-member-empty-iff,
length_one,
squash_wf,
true_wf,
iff_weakening_equal,
bag-member-single
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
sqequalRule,
baseClosed,
independent_functionElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
lambdaEquality,
setElimination,
rename,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
productElimination,
promote_hyp,
hyp_replacement,
Error :applyLambdaEquality,
axiomEquality,
universeEquality,
dependent_set_memberEquality,
imageMemberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. single-valued-bag(b;T) supposing \#(b) \mleq{} 1
Date html generated:
2016_10_25-AM-10_29_23
Last ObjectModification:
2016_07_12-AM-06_45_36
Theory : bags
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