Nuprl Lemma : bag-only_wf
∀[T:Type]. ∀[bs:bag(T)]. only(bs) ∈ T supposing #(bs) = 1 ∈ ℤ
Proof
Definitions occuring in Statement :
bag-only: only(bs),
bag-size: #(bs),
bag: bag(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,
bag: bag(T),
all: ∀x:A. B[x],
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
bag-size: #(bs),
bag-only: only(bs),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
nat: ℕ,
uiff: uiff(P;Q),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
member-permutation,
pos_length2,
hd_member,
length-one-member,
bag_wf,
nat_wf,
bag-size_wf,
equal_wf,
true_wf,
squash_wf,
member_wf,
equal-wf-base,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
hd_wf,
permutation-length,
permutation_weakening,
permutation_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
promote_hyp,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
because_Cache,
dependent_functionElimination,
independent_isectElimination,
pointwiseFunctionality,
sqequalRule,
pertypeElimination,
productElimination,
cumulativity,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
productEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
axiomEquality,
setElimination,
rename,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[bs:bag(T)]. only(bs) \mmember{} T supposing \#(bs) = 1
Date html generated:
2016_05_15-PM-02_34_51
Last ObjectModification:
2016_01_16-AM-08_53_09
Theory : bags
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