Nuprl Lemma : list_ind_reverse_wf
∀[A,B:Type]. ∀[L:A List]. ∀[nilcase:B]. ∀[F:B ⟶ (A List) ⟶ A ⟶ B]. (list_ind_reverse(L;nilcase;F) ∈ B)
Proof
Definitions occuring in Statement :
list_ind_reverse: list_ind_reverse(L;nilcase;R),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_ind_reverse: list_ind_reverse(L;nilcase;R),
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
squash: ↓T,
int_iseg: {i...j},
cand: A c∧ B,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
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,
equal-wf-T-base,
nat_wf,
length_wf_nat,
less_than_transitivity1,
less_than_irreflexivity,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_subtype_base,
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,
intformeq_wf,
int_formula_prop_eq_lemma,
firstn_wf,
last_wf,
length_wf,
eqtt_to_assert,
assert_of_eq_int,
le_wf,
squash_wf,
true_wf,
length_firstn_eq,
iff_weakening_equal,
length_firstn,
non_null_iff_length,
subtype_rel_list,
top_wf,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
comment,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
hypothesisEquality,
extract_by_obid,
isectElimination,
thin,
isect_memberEquality,
because_Cache,
universeEquality,
lambdaFormation,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
applyEquality,
baseClosed,
unionElimination,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
functionExtensionality,
applyLambdaEquality,
imageElimination,
dependent_set_memberEquality,
productEquality,
imageMemberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:A List]. \mforall{}[nilcase:B]. \mforall{}[F:B {}\mrightarrow{} (A List) {}\mrightarrow{} A {}\mrightarrow{} B].
(list\_ind\_reverse(L;nilcase;F) \mmember{} B)
Date html generated:
2017_04_17-AM-08_43_46
Last ObjectModification:
2017_02_27-PM-05_03_21
Theory : list_1
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