Nuprl Lemma : has-value-length-member-list
∀[l:Base]. l ∈ Base List supposing (||l||)↓
Proof
Definitions occuring in Statement :
length: ||as||,
list: T List,
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
bfalse: ff,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
guard: {T},
sq_type: SQType(T),
compose: f o g,
or: P ∨ Q,
decidable: Dec(P),
subtype_rel: A ⊆r B,
prop: ℙ,
and: P ∧ Q,
top: Top,
all: ∀x:A. B[x],
not: ¬A,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
list_ind: list_ind,
length: ||as||,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
has-value: (a)↓,
cons: [a / b],
nil: [],
it: ⋅
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
bool_subtype_base,
bool_wf,
subtype_base_sq,
bool_cases,
equal-wf-base,
not_wf,
bnot_wf,
assert_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
eq_int_wf,
le_wf,
fun_exp_unroll,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
subtract_wf,
decidable__le,
bottom_diverge,
strictness-apply,
fun_exp0_lemma,
base_wf,
int_subtype_base,
has-value_wf_base,
less_than_wf,
ge_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_properties,
has-value-implies-dec-ispair,
cons_wf,
value-type-has-value,
int-value-type,
nil_wf,
has-value-implies-dec-isaxiom
Rules used in proof :
impliesFunctionality,
productElimination,
cumulativity,
because_Cache,
dependent_set_memberEquality,
unionElimination,
applyEquality,
baseClosed,
closedConclusion,
baseApply,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
independent_functionElimination,
computeAll,
independent_pairFormation,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
lambdaFormation,
intWeakElimination,
rename,
setElimination,
hypothesisEquality,
isectElimination,
extract_by_obid,
thin,
compactness,
hypothesis,
sqequalRule,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
callbyvalueReduce,
callbyvalueCallbyvalue,
callbyvalueAdd
Latex:
\mforall{}[l:Base]. l \mmember{} Base List supposing (||l||)\mdownarrow{}
Date html generated:
2020_05_20-AM-09_07_31
Last ObjectModification:
2020_01_26-PM-00_13_22
Theory : bar!type
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