Nuprl Lemma : islist-implies-is-list
∀[t:Base]. t ∈ Base List supposing islist(t)
Proof
Definitions occuring in Statement :
islist: islist(t),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
islist: islist(t),
eval_list: eval_list(t),
list_ind: list_ind,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
compose: f o g,
sq_type: SQType(T),
guard: {T},
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bfalse: ff,
has-value: (a)↓,
cons: [a / b],
nil: [],
it: ⋅
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
has-value_wf_base,
int_subtype_base,
base_wf,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
fun_exp_unroll,
le_wf,
islist_wf,
eq_int_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
assert_wf,
bnot_wf,
not_wf,
equal-wf-base,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
has-value-implies-dec-ispair-2,
top_wf,
cons_wf,
has-value-implies-dec-isaxiom-2,
nil_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
compactness,
thin,
extract_by_obid,
isectElimination,
hypothesisEquality,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
unionElimination,
dependent_set_memberEquality,
because_Cache,
cumulativity,
productElimination,
impliesFunctionality,
callbyvalueCallbyvalue,
callbyvalueReduce
Latex:
\mforall{}[t:Base]. t \mmember{} Base List supposing islist(t)
Date html generated:
2018_05_21-PM-10_18_50
Last ObjectModification:
2017_07_26-PM-06_36_45
Theory : eval!all
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