Nuprl Lemma : tuple-type-append-equipollent
∀L1,L2:Type List. tuple-type(L1) × tuple-type(L2) ~ tuple-type(L1 @ L2)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
tuple-type: tuple-type(L),
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
nat: ℕ
Lemmas referenced :
list_induction,
all_wf,
list_wf,
equipollent_wf,
tuple-type_wf,
append_wf,
tupletype_nil_lemma,
list_ind_nil_lemma,
istype-void,
tupletype_cons_lemma,
list_ind_cons_lemma,
equipollent-identity,
unit_wf2,
equipollent_same,
null_wf,
uiff_transitivity,
equal-wf-T-base,
bool_wf,
assert_wf,
eqtt_to_assert,
assert_of_null,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
append_is_nil,
equipollent_functionality_wrt_equipollent2,
product_functionality_wrt_equipollent_right,
equipollent_inversion,
length_wf_nat,
nat_wf,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
equipollent_functionality_wrt_equipollent,
equipollent-product-com,
equipollent_weakening_ext-eq,
ext-eq_weakening,
equipollent-product-assoc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
sqequalRule,
Error :lambdaEquality_alt,
hypothesis,
productEquality,
hypothesisEquality,
applyEquality,
cumulativity,
Error :inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
because_Cache,
Error :universeIsType,
independent_functionElimination,
dependent_functionElimination,
Error :isect_memberEquality_alt,
voidElimination,
rename,
Error :functionIsType,
unionElimination,
equalityElimination,
baseClosed,
productElimination,
independent_isectElimination,
independent_pairFormation,
Error :equalityIsType3,
Error :equalityIsType1,
Error :dependent_set_memberEquality_alt,
Error :equalityIsType4,
intEquality,
natural_numberEquality,
hyp_replacement,
applyLambdaEquality,
setElimination
Latex:
\mforall{}L1,L2:Type List. tuple-type(L1) \mtimes{} tuple-type(L2) \msim{} tuple-type(L1 @ L2)
Date html generated:
2019_06_20-PM-02_19_23
Last ObjectModification:
2018_10_06-AM-11_23_57
Theory : equipollence!!cardinality!
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