Nuprl Lemma : select?_wf
∀[A:Type]. ∀[as:A List]. ∀[a:A]. ∀[i:ℕ]. (as[i]?a ∈ A)
Proof
Definitions occuring in Statement :
select?: as[i]?a,
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
select?: as[i]?a,
nat: ℕ,
uimplies: b supposing a,
ge: i ≥ j ,
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,
and: P ∧ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T}
Lemmas referenced :
nat_wf,
list_wf,
lt_int_wf,
length_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
less_than_wf,
select_wf,
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,
le_int_wf,
le_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
cumulativity,
universeEquality,
setElimination,
rename,
baseClosed,
independent_isectElimination,
dependent_functionElimination,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
equalityElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}[as:A List]. \mforall{}[a:A]. \mforall{}[i:\mBbbN{}]. (as[i]?a \mmember{} A)
Date html generated:
2018_05_22-AM-00_20_52
Last ObjectModification:
2017_07_26-PM-06_55_24
Theory : rationals
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