Nuprl Lemma : select-add-indices
∀[T:Type]. ∀[L:T List]. ∀[i:ℕ||L||]. (add-indices(L)[i] = <i, L[i]> ∈ (ℕ||L|| × T))
Proof
Definitions occuring in Statement :
add-indices: add-indices(L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
add-indices: add-indices(L),
top: Top,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
prop: ℙ,
squash: ↓T,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
cand: A c∧ B,
ge: i ≥ j ,
nat: ℕ,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
label: ...$L... t
Lemmas referenced :
select-map,
upto_wf,
length_wf,
subtype_rel_list,
top_wf,
length_upto,
length_wf_nat,
lelt_wf,
int_seg_wf,
equal_wf,
squash_wf,
true_wf,
select_wf,
int_seg_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,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
le_wf,
less_than_wf,
select_upto,
non_neg_length,
nat_properties,
iff_weakening_equal,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
cumulativity,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
independent_isectElimination,
lambdaEquality,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
imageElimination,
equalityTransitivity,
equalitySymmetry,
productEquality,
natural_numberEquality,
independent_pairEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
computeAll,
applyLambdaEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
universeEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[i:\mBbbN{}||L||]. (add-indices(L)[i] = <i, L[i]>)
Date html generated:
2018_05_21-PM-07_33_15
Last ObjectModification:
2017_07_26-PM-05_08_09
Theory : general
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