Nuprl Lemma : list-ext
∀[A:Type]. A List ≡ Unit ⋃ (A × (A List))
Proof
Definitions occuring in Statement :
list: T List,
b-union: A ⋃ B,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
unit: Unit,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
btrue: tt,
all: ∀x:A. B[x],
implies: P ⇒ Q,
it: ⋅,
uiff: uiff(P;Q),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
colength: colength(L),
has-value: (a)↓
Lemmas referenced :
colist-ext,
colist_wf,
has-value_wf-partial,
nat_wf,
set-value-type,
le_wf,
int-value-type,
colength_wf,
b-union_wf,
unit_wf2,
btrue_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
bfalse_wf,
subtype_partial_sqtype_base,
set_subtype_base,
int_subtype_base,
value-type-has-value,
subtype_rel_b-union-left,
subtype_rel_transitivity,
has-value_wf_base,
is-exception_wf,
subtype_rel_b-union-right,
termination
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_pairFormation,
productElimination,
promote_hyp,
lambdaEquality,
setEquality,
cumulativity,
independent_isectElimination,
intEquality,
natural_numberEquality,
because_Cache,
productEquality,
universeEquality,
setElimination,
rename,
hypothesis_subsumption,
applyEquality,
imageElimination,
unionElimination,
equalityElimination,
imageMemberEquality,
dependent_pairEquality,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
dependent_pairFormation,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
baseClosed,
independent_pairEquality,
callbyvalueAdd,
dependent_set_memberEquality,
divergentSqle,
sqleReflexivity,
addEquality
Latex:
\mforall{}[A:Type]. A List \mequiv{} Unit \mcup{} (A \mtimes{} (A List))
Date html generated:
2017_04_14-AM-07_54_14
Last ObjectModification:
2017_02_27-PM-03_21_08
Theory : list_0
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