Nuprl Lemma : bag-member-select
∀[A:Type]. ∀[L:A List]. ∀[i:ℕ||L||]. L[i] ↓∈ L
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-member: x ↓∈ bs,
exists: ∃x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
prop: ℙ,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
list-subtype-bag,
select_member,
equal_wf,
bag_wf,
l_member_wf,
select_wf,
int_seg_properties,
length_wf,
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,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_pairFormation,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
lambdaEquality,
hypothesis,
sqequalRule,
independent_pairFormation,
dependent_functionElimination,
productEquality,
cumulativity,
setElimination,
rename,
natural_numberEquality,
productElimination,
unionElimination,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
imageElimination,
imageMemberEquality,
baseClosed,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[L:A List]. \mforall{}[i:\mBbbN{}||L||]. L[i] \mdownarrow{}\mmember{} L
Date html generated:
2017_10_01-AM-08_53_57
Last ObjectModification:
2017_07_26-PM-04_35_45
Theory : bags
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