Nuprl Lemma : select-bag-rep
∀[T:Type]. ∀[n:ℕ]. ∀[x:T]. ∀[i:ℕn]. (bag-rep(n;x)[i] = x ∈ T)
Proof
Definitions occuring in Statement :
bag-rep: bag-rep(n;x),
select: L[n],
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
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,
prop: ℙ,
bag-size: #(bs),
l_member: (x ∈ l),
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
cand: A c∧ B
Lemmas referenced :
member-bag-rep,
select_wf,
bag-rep_wf,
int_seg_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
bag-size-rep,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
list-member-bag-member,
int_seg_subtype_nat,
false_wf,
less_than_wf,
length_wf,
equal_wf,
int_seg_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
cumulativity,
hypothesis,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
lambdaFormation,
productEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[x:T]. \mforall{}[i:\mBbbN{}n]. (bag-rep(n;x)[i] = x)
Date html generated:
2017_10_01-AM-08_55_02
Last ObjectModification:
2017_07_26-PM-04_36_54
Theory : bags
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