Nuprl Lemma : recode-tuple_wf
∀[f:TypeRecoding]. (recode-tuple(f) ∈ TupleRecoding)
Proof
Definitions occuring in Statement :
recode-tuple: recode-tuple(f),
tuple-recoding: TupleRecoding,
type-recoding: TypeRecoding,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
recode-tuple: recode-tuple(f),
tuple-recoding: TupleRecoding,
type-recoding: TypeRecoding,
uall: ∀[x:A]. B[x],
member: t ∈ T,
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},
or: P ∨ Q,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
decidable: Dec(P),
nil: [],
it: ⋅,
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
spreadn: spread3,
bool: 𝔹,
unit: Unit,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
true: True,
iff: P ⇐⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
rev_implies: P ⇐ Q,
bnot: ¬bb,
assert: ↑b
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,
equal-wf-T-base,
nat_wf,
colength_wf_list,
less_than_transitivity1,
less_than_irreflexivity,
list-cases,
tupletype_nil_lemma,
list_ind_nil_lemma,
nil_wf,
unit_wf2,
equal-unit,
all_wf,
equal_wf,
tuple-type_wf,
product_subtype_list,
spread_cons_lemma,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
tupletype_cons_lemma,
list_ind_cons_lemma,
list_wf,
null_wf3,
subtype_rel_list,
top_wf,
bool_wf,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_null,
decidable__lt,
length_wf,
append_wf,
append-tuple_wf,
length_of_nil_lemma,
squash_wf,
true_wf,
iff_weakening_equal,
split-tuple_wf,
non_neg_length,
length-append,
lelt_wf,
subtype_rel_self,
firstn_append,
split-tuple-append-tuple,
null_nil_lemma,
length_of_cons_lemma,
null_cons_lemma,
cons_wf,
firstn_wf,
nth_tl_wf,
subtype_rel-equal,
append-nil,
append-tuple-zero,
eq_int_wf,
assert_of_eq_int,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
applyEquality,
because_Cache,
unionElimination,
dependent_pairEquality,
dependent_set_memberEquality,
functionExtensionality,
setEquality,
functionEquality,
productEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyLambdaEquality,
addEquality,
baseClosed,
cumulativity,
imageElimination,
equalityElimination,
spreadEquality,
independent_pairEquality,
imageMemberEquality,
impliesFunctionality,
hyp_replacement
Latex:
\mforall{}[f:TypeRecoding]. (recode-tuple(f) \mmember{} TupleRecoding)
Date html generated:
2018_05_21-PM-08_03_34
Last ObjectModification:
2017_07_26-PM-05_39_40
Theory : general
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