Nuprl Lemma : list_update_wf
∀[T:Type]. ∀[l:T List]. ∀[i:ℤ]. ∀[x:T]. (l[i:=x] ∈ T List)
Proof
Definitions occuring in Statement :
list_update: l[i:=x],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
list_update: l[i:=x],
update: f[x:=v],
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
nequal: a ≠ b ∈ T ,
lelt: i ≤ j < k,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T
Lemmas referenced :
mklist_wf,
length_wf_nat,
eq_int_wf,
bool_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
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,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
setElimination,
rename,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
natural_numberEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[i:\mBbbZ{}]. \mforall{}[x:T]. (l[i:=x] \mmember{} T List)
Date html generated:
2018_05_21-PM-06_46_10
Last ObjectModification:
2017_07_26-PM-04_55_57
Theory : general
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